You're not going to be able to run recent games on it, really. You're running on Intel integrated chip with a low clock speed processor. The SSD doesn't have much impact on gaming other than load times.
It isn't a gaming computer, but that doesn't mean you can't play games on it. Look into older titles, and observe the recommended system requirements. If you aren't content with any older titles that aren't as intensive and you want to be able to run the more intensive older titles (original Crysis, etc) or new titles, I would buy either a PC desktop or a budget laptop. It doesn't have to be a "gaming laptop," you can pick up a notebook with a 1GB dedicated card for considerably cheap.
My 11” Air is a gaming computer—it’s one of the things I bought it for, in fact. I don’t expect to run the VERY latest games at the highest (or even medium) detail, but I can run really awesome games at really awesome detail levels—and I do. IdTech 4 games (Quake Wars) and BioShock, mainly, both of which look great and run will once you find the right settings. (Figuring out what settings really affect the look the most, vs. what settings impact performance the most. The balance I’ve found is far better than I expected!) As for other games, people were getting StarCraft 2 to run decently on last year’s models, and for games, this year’s seem to perform about the same (although in some cases the new CPUs will help). It’s not the phrase “integrated graphics” that matters, and it doesn’t matter what Intel delivered in the past, either. It matters what this machine and these Intel chips deliver now. And I am a very happy gamer!
Best of all, it’s a gaming machine I take anywhere amazingly easily! With a pocket projector along for the ride (soon).
Not every serious gamer is best served by an Air, of course. But for some serious gamers, it’s ideal! You have to choose what fits your goals. Fun, for me, doesn’t come from benchmarks or even the latest shader effects (which are awesome but not vital). Or even playing whatever game that just game out—as though last year’s games are not fun in some way. Fun doesn’t come from bragging rights. But it does, sometimes, come from whether I actually have my laptop WITH me or not! Portability is great in those situations. I can grab my Air without a second thought, compared to heavy game-centric machine.
As for a Thunderbolt dock... sign me up! Have my cake and eat it too! It won’t come from Apple—but from third parties? I have little doubt.