Firstly I applaud your openness and willingness to take a risk and post this, hopefully gaining some useful input.
As you asked I'll post aspects that I found concerning along with suggestions, make of them what you will.
One aspect that really applies to everything I discuss below, is that you seem to have just implemented the first idea that came into your head, that nothing has had several passes or re-designs applied. You made your logo's using the same font with no more thought given to them. That you probably made this trailer as your first attempt and thats it. Though this may feel overly critical, it is meant to instead high-light that such an approach will rarely if ever produce anything good. Its pretty established that to get the best design and outcome you need to work up several ideas and re-factor them afterwards, itteratively improving the concepts. Indeed without making several attempts/passes of each aspect below, you wouldn't know what works best. Of course this is time consuming and can be frustrating, but usually it does improve the end result.
Actually a good example of this procedure would be this reply as it has become a wall of text. A second pass through it should be able to streamline my points and include more succinct clearer examples. However I don't have the time to do so, and its not like i'm trying to sell you anything ;)
Shogun3D / Logo
As a company name its rather weird, not sure if you can change it? The first thing that comes to mind with Shogun is Total War, which is not really good for 'your' company recognition. The actual logo is extremely basic and barely deserves to be called a logo ;) It appears to be the same font as all the other text so it doesn't stand out or differentiate itself in anyway. Plus what is with the size of the TM, should be much smaller.
Your first step should be a competent redesign of the logo, perhaps even search the web for designers offering free logo design services. You will probably also need to determine what you want your logo to 'say' about yourself as a company, what influences might affect its design etc.
Loop-Til / Logo
This is better, but again the name would be vastly improved if it was more unique, using a different font. Indeed with the nature of the game I would certainly look towards more rounded modern style fonts for it.
I do like (maybe even love) the inclusion of the graphic that essential explains what the game is all about. I think this alone could work very well, especially if animated to show the loop forming. I might consider aligning it to the end of the game title though it looks odd everything being centered horizontally and the graphic is pretty big. Actually having both the title and the graphic roughly the same size/area makes it difficult to determine which is most important, there is no difference in weight or gravitas between them, meaning my eye is constantly flipping back and forth between them on screen.
You know I really think this title logo offers a massive opportunity for creating something very interesting, if you can give it time and perhaps find someone willing to turn it into a full on animated logo ( should be easily enough in Flash, then outputed to frames or video). For example I could easily see the graphic not appearing at first at all, but the line forming/animating out of the end of the title logo, animating/drawing into the loop you have. Perhaps the three squares are already visible and gently oscillating in place, with the loop line forming and drawing around them?
The reason I find this interesting is that you can essentially explain the entire game concept through its animated logo.
Overall the trailer feels unfinished, for many reasons and somewhat amateur on many levels which I think damage it. Whilst I could and will list a few points to consider, your best bet would be to spend some time investigating and analysing other trailers for similar or even dis-similar products to understand how you could improve yours.
Buy Fraps, its dirt cheap or maybe download Microsoft Expressions Recorder (it was free for up to 10 min of screen recording at a time, no water marks), re-record without the watermarks and developer data. Record at a relatively high resolution (e.g. 720p) or maybe natively if its design for say mobile with a much lower resolution - though I would maybe argue you should produce a new build that supports high resolutions and be able to change the relative size of gui elements (e.g. the score) if they are too small to read at a high resolution.
One approach when making a trailer which may help is to consider it as a short story, that you want to use the visuals, text, audio, to convey the game in a fashion that follows traditional story telling. I mean even news reports these days have a start, middle and end, often being constructed to conform to telling a story rather than informing on the actual news event. Now I don't mean you actually create a story, have a hero, save the girl etc, just use the concept of story telling, to inform the trailer, which also applies to pacing/timing, build up tension, release etc. Though i'd also argue that such constructs should probably be in the game too, as a means of introducing the game to players and not simply jumping into the middle of it.
For example, the first few shots of the game could show a much simpler part of the game, not as cluttered, maybe not even having any of the dots to collect on screen at all, serving as an introduction to what the player controls. Next you';d show a few dots on screen, and simple game play such as tagging the green ones, then building up to show loops to capture the red dots and finally show the game over condition.
At each of the stages above, explain with simple text (could be simple bullet points in nature, though not in terms of display) or a voice over what is happening, explain that you control the loop line, explain what the green dots are and why you need to collect them, explain what the red dots represent and why you must capture them, then show the difficulty ramping up, with you capturing larger numbers of red dots etc and finally what the game over conditions is ( I found it unclear on the video, perhaps when you make a loop that captures nothing?).
By thinking in these terms you should also be able to improve the pacing of the trailer, so that it builds up in tension or excitement, towards the climax of the 'end game'. Audio can really help here too, though you are often limited by using off the shelf music tracks as normally these will dictate the pace, cuts etc. However you may be able to edit the audio to match your own vision of the trailer, i.e you could cut to re-arrange the music, fade in/out, add effects etc.
You could even go full out and make special records using a special build of the game in order to high-light or allow yourself to 'tell a story' better. For example a build that increases the size of the player, so you can effectively have a zoomed in view of the player dot making the loop. This change of scale would add to the visual interest of the trailer video and could have the player dot star as a dot, then draw out a line or loop (this might also add some feeling of 'character' to the player controlled dot). The same technique could be used to create more visual interest when showing off other aspects of the game, such as a quick cut to a zoomed in area of the red dots exploding. Again its all about changes to the visual pace being shown, that the whole video is not on the same 'level/plane/scale' so to speak. Think of TV or Film and all the ways they make what can essentially be boring scenes more interesting, e.g. different aspects, such as close-ups, distant shots etc and how that could be applied to your trailer.
Other aspects to consider is maybe dropping the company logo and even the title from the start of the video as they delay the viewer from seeing the most important aspect of the trailer - the gameplay. The logos could happen after an establishing shot of the game, or even at the end of the trailer.
I'd also consider the potential of including some bits or even making a secondary trailer that features someone playing the game, or perhaps someone playing and another watching, to capture their response to it. I suggest this because based on game play footage alone it doesn't look that thrilling to play, yet in reality it might be. It may just be that magical combination of simplicity and fun that makes it a game that's impossible to put down once you've started, it may illicit 'oohs and arrs' from the player or watchers. The only way to show this though is to have some video of people playing the game. I think a good example of how this can 'sell' a game would be this video for SpaceTeam, though not a great trailer it accomplishes its aim which is to 'sell' the multi-player/social aspect.
Finally, although you've stated and clearly set out to make a minimalist looking designed and styled game, to me visually it feels like something i'd see from a 24h game contest. So much so that before releasing the game I would seriously suggest re-evaluating what you could do with the visual style to improve it, make it prettier and more appealing.
As such I'd be very tempted to look at adding a more distinctive style to the game, embellishing the graphics somewhat, perhaps making the score more prominent and visually interesting. Maybe increase the resolution of the loop line, make the loop change colour when you collect a green dot or capture red dots. Not only would doing this increase visual feedback to the player it will make it more visually interesting without losing the minimalist nature.
Its hard to tell from what you've posted but the game itself appears to be on just one level, that is, there is no variation in the game as you progress. So although the initial concept may well be fun to play, I would question whether it can maintain that fun if everything is the same? For example some question i'd ask are,
Why are red and green both square dots?
Why are red and green dots the same size?
Why are all the dots the same size all the time? Do they change size? Can changing size on different levels or within a level add or alter the game play mechanics?
What other dots can there be, what other colours and what gameplay aspects could they add?
If you do have more interesting game play mechanics later in the game, then these should be show cased in the trailer, if you don't then perhaps you should consider adding some?
In a similar view could you build in 'character' to the player controlled dot? I don't mean turn the dot into a character sprite or anything, but to give it some character, something more than a simple dot. Doing so would certainly make it easier to build a trailer around it as it gives you more leverage to use it on building up scenes. Again i'm not really talking Pixar level of characterization, but just something more than simply bam you are moving this dot. e.g. as mentioned above that perhaps at the start of the game you just have the dot, maybe it pulsates a bit, then as you move the dot it leaves the trail etc. Heck you could go full out and have the 'dot' discover it can create a trail and capture the evil red dots or something ;)
Anyway I wish you luck with your project. The game certainly looks interesting at this stage, but I feel and fear you'll have to do much more to the trailer, logo's and the game style to make it appealing to a wider audience. After all you only get once chance to make a first impression.