Firstly, video game music is a very deep topic, and people have done very sophisticated things with it. Nowadays it runs the full gamut from simply playing one MP3 in a loop, to procedurally generating full arrangements on the fly. One example from the early 90s is LucasArts' iMuse system, which seamlessly arranges music to fit with gameplay.
You have choices that you can discuss with your programmer. For example you could potentially solve your problem with reverb by having some basic multitracking in the game's audio engine, and reverb added at playback time.
However, let's assume for now that you're restricted to providing ready-mixed music samples, and all the game engine can do is sequence the order in which they're played.
Let's say you have three sections, A (intro), B (intended to loop), C (ending).
The first task is to make sure that B loops cleanly. To do that, if B is 16 bars long, record 48 bars, and take the middle 16 as your loop. When it loops, the reverb from the first discarded part will convincingly work as the reverb for the end of what you've kept. You may need to tweak the wave a little -- but less often than you'd imagine. Let's call this sample B0
The second task is to get a clean transition from A into B. Perform a take of A transitioning into B. Use A. Use B - let's call it B1.
So now to get a clean piece of music, the programmer needs to schedule
A, B1, loop(B0)
If we do something similar with the outtro, the programmer needs to, when the level is ending, move from B0 to B2, to C. To get to the ending sooner, he could switch (or fade) from B0 to the corresponding part of B1.
You could actually get all these sections by making a recording of A,B,B,B,C and slicing that up. You can probably see that by chopping into smaller sections, you could have less repetition in the sections, and so use less memory.
You can pretty much guarantee a loopable sample if you record a section dry, loop it, add reverb etc. at mixdown, and slice your sample out of that mixdown.
It's worth noting that in some kinds of game, jolting musical changes are acceptable. When you cross the finish line in Sonic the Hedgehog, it cuts instantly to a fanfare with no regard for the rhythm of the music that was playing before. When you pick up the star in Mario, the star fanfare plays immediately, then the double-speed music starts with no regard for where the tune was previously.