The A900 will definitely be good for trance and games, and more than that besides. It's one headphone that takes pretty much every genre in stride and gives you back good performance. I think that the DT770 is better for games, amped or unamped, and I did a bit of testing myself to check this out. The DT770 doesn't lose it's razor-sharp imaging ability unamped, but it does lose a lot of the bass, and it's tone becomes thin and even more strident that usual. The A900 doesn't image as precisely as the DT770, and isn't quite as great for competitive games - but it's still great, head and shoulders above the HD600, for instance, which doesn't image well with games at all - not because it can't, but because it's recessed treble masks footsteps and other relevent information. For music, of course, the DT770 unamped was not pleasant, though not terrible. The A900 unamped would be a much better choice there.
Anyway, the A900 is one great set of cans, and it won't disappoint. Be sure to burn them in - they won't reach anywhere near their sonic potential until you have at least 50 hours on them, possibly more. The highs are a bit steely out of the box and the bass is a bit loose. With burn-in, the highs settle down and mellow out, while the bass becomes tighter and better defined. The midrange is a little recessed, and there is an upper midrange coloration due to their closed nature, but you can't have everything, especially with a closed headphone at that price. They're still way better balanced than the DT770 and better for music overall.