Quite honestly the most important way to learn while programming, I've found anyway, is to try things, and to have them not work. That's part of learning how gamedev works as well, if you want to make games as a coder your goal should be to learn what goes into a game and then you will have an easier time understanding what really makes up a game engine and how to compare features between them.

I think there really is no substitute for actually making a game and the advice oft repeated on here(and by myself) is to start at the basics, make pong, make breakout, something like that. I highly recommend using something like C# with XNA to get your feet wet to what the basic pieces of a game engine are, there's just too much to explain without experiencing it firsthand. You'd be surprised how much there is in common between pong and Unreal tournament or something, but the code abstraction is there, between many games there are major systems in place that are always in place, game logic is often very disjointed from engine logic.

One of the biggest problems is that people are cocky without even thinking they are, they think "oh I know it's hard, I know its a lot of work, if I just persevere I can do it!" But no, really, if you make a few games even simple ones your view of the 20 story tall gorilla will do nothing but grow. But really there's no substitute for experience, you could pick a "major" engine like UDK or Unity but as you get deeper into developing your game you will realize there is so much you do not understand enough to make decisions on.

My advice: make your goal to -learn- to make games, not to set your eyes on one particular game you always wanted to make, you'll just get frustrated with your slow progress or feel like you aren't working towards that super goal and it will really hurt you in the long run. Don't try to learn math by solving a whiteboard length equation, learn math by starting at counting.