So at the start of this E3 week. One of the people on my team and started talking about stuff on discord. Another one came in and they started arguing with each other. I felt like I should've said something, but I didn't know what and thought maybe it would be better to give them some time to breathe or whatever, but the next morning I saw them arguing again and one said he'll go somewhere else and the other told him to #*@! off. It feels pretty akward going into that discord now. I have to say something to get us progressing, but I'm not sure how to follow up after that fight. How have y'all dealt with something like this?

If you haven't figured out yet, Computer Scientists are extremely relatable, charismatic, and always open-minded to new ideas, or different perspectives that challenge a lot of their pre conceived notions.  

In summation, these things happen. Most of the time they'll naturally blow over. In the off chance it doesn't, and you are in some form of position to where you are expected to, "lead" the team, you need to break up the ruler contest. Sometimes you need to pull rank, and tell everyone to focus on their work. When you're a manager, or team lead, you can't expect to always be friends, or buddy-buddy with your co-workers.

If this is a small development house, or no one who occupies a role as a, "lead" then maybe there needs to be one?

Also, remember to put things into perspective for them. Is this point of contention they are fixated on trivial? Is it something you'd expect mature adults to walk away from for a day to have let go, or to have seen the others perspective?

A suggestion to solving this problem is bringing on a team leader that isn't afraid to step in and set things straight. Motivation to make a game is different but straight arrogance to ruin a potential project wouldn't even stand in the real world of business. Either you or someone needs to get it worked out between the two, or you may have to find talent elsewhere. Of course this also ties into personal issues, non of us were there and can't truly understand what happened. But essentially you need someone to kinda guide the team in the right direction. Hope this helps!  

This ties into what @Tom Sloper was saying so I'm gonna give him a one-up so I don't feel like I'm stealing his response. 

Yeah, this is just a hobbyist team and I was the one to put this together and well just communicate on discord so yeah I have to be the one to say something. I'm just not sure how to start out. It's really awkward. They were fussing about movement scripts and one wanted to completely change my plans for the 1st level. I'm struggling if I want to let that one guy go since I have to look for more people anyway.

If he wants to change everything and have full control, then I don't believe he is at all an asset to the TEAM.. after-all this is a team project and if its going to be on a hobbyist level the least you could take away from it is team-work knowledge. Some people don't understand that there's more than just work to get done, there are morals and ethical beliefs all different from each member, there are feelings to be hurt, someone who helped tirelessly on the previous movement script has just been told its trash and the other guy wants it completely redone, this affects the member who wrote the old code. There are time schedules to be met, you can't be wasting hobby time arguing about how things should get done. There are expectations to be met, this goes for a team and work basis.  

CASE 1: The Aggressive member is being.. well.. an a*hole. 

 Talk to the aggressive member of the team, explain to him that this is still a team project no matter what, you need to tell him that complete systems can't just be re-written because there's something that doesn't make sense or you "think" or know it really does suck. There are better approaches that make you professional and well liked. I would approach this by making the member suggest different methods or ways to complete a problem that they don't like or understand. (NOT a re-write, but , considering graphics libraries were never designed for "hit x and this square will show up".. there are thousands of ways to do things,  unless your on some God level of Graphics programming out of the womb, you will 100% gain experience by listening to other approaches of doing things. 

CASE 2: Each member needs to know how to take criticism. 

The non aggressive member who was told the control systems may need to be re-written has taken this to great offence, and now despises the other member for their words of knowledge. In which case you need to sit the less aggressive member down and tell him that criticism is part of the process and he has to learn to handle it a little better than by taking offence to everything. This makes you a better coder, and a better human. Knowing how to gauge and handle other peoples criticism will send you rocketing in your career and life. 

CASE 3: Your just wasting your time otherwise. If it gets out of hand then its time to play baby sitter and monitor the calls between the two, if theyre arguing on their own time then whatever, but if they're constantly arguing on project time, there's a major issue. Id say you struck gold with this situation, handling these kinds of things face on makes you a better leader in life, everyone leads at one point, so be a good one. When I say monitor I mean keep track of there fighting on project time, if they're fighting way to much you're holding yourself back by chasing them all over. 

PS. I've started some great friendships that started as arguments, and strong hate, but then moved towards a realization that we both just wanted the same goal and decided to put aside the small amount of despise for the person in order to gain an amazing and knowledgeable friend.