I've found they've gotten pretty good. I have a 7970 and a couple of R290 GPUs, as well as whatever ATI GPU is in my laptop (a 6000 series Mobility GPU), they all seem to work fine under Linux. Admittedly, I don't do a lot of gaming, though I just bought a few new games in the winter sale, since they've added so many Linux games (and some of them are freakin' awesome games).
I haven't actually tried any of the really tough games, like Half Life or whatever yet...but, I'm actually super excited about playing Left 4 Dead 2 on Linux on one of the new GPUs. So, we'll see soon enough.
I have a ATI Mobility Radeon HD 4650(not very powerful and quite old now) and I can play Dota 2,Left4Dead and other games on windows with no problem at all,while on Linux(Ubuntu 13.10) I can barely open the games.
I haven't actually tried any of the really tough games, like Half Life or whatever yet...but, I'm actually super excited about playing Left 4 Dead 2 on Linux on one of the new GPUs. So, we'll see soon enough.