There don't seem to be a lot of gamers in these forums so you may not get the answer here. I think your best bet is to either contact the games' developers or ask in their forums like this one if they have it.
My son is a hardcore gamer (you name the platform and he uses it) and, when he needs hardware info about compatibility of his iMac, he goes to the game companies and their users and always gets a fast answer.
If you're a serious high end gamer, probably not.
For gamers and high end games 512 MB VRAM graphics are usually a minimum spec.
Typically, for more expandbility and graphics power, you will need to look at the 27 inch screen models and use the build to order options.
The graphics cards availble for the 27 inch iMac are a 1 GB or 2 GB VRAM graphics engine.
The minimum I would recommend is the 1 GB card. If your budget allows, order a 27 inch iMac with the 2 GB VRAM graphics card.
Though i am not a gamer, i would like to be able to play any game i wish on my device (and i can't afford the 27 inch) .
Is the base 21.5'' model enough or not......
I've asked myself the same question because I just ordered a 27" 3.4 GHZ i7 with the high end graphics card (NVIDIAGeFrc GTX 680MX 2G GDDR5) and was thinking that it certainly should be fast enough to run games available for the Mac platform. My search revealed that getting an answer to that question isn't a simple chore.
What others have said is true, one must ask the developer of the game what their requirements are and whether or not some specifics are required.
For example, some games still sold today that were originally released years ago one would certainly think would run well on a modern Mac platform using a more modern graphics engine but this is not necessarily true. Some of those old games require a PowerPC and, while most of them will run on an Intel Mac platform running Snow Leopard or earlier using Rosetta--an emulator for PowerPC code that Apple made available in earlier versions of OS X--Rosetta was discontinued after Snow Leopard. If you're using a more recent version of OS X (Lion or Mountain Lion) then the OS does not provide Rosetta and the game won't execute.
Another problem is that some game developers working on the Mac platform wrote code exclusively for certain specific graphics cards and the chances of their product executing properly on other cards is not necessarily 100%. Again, only the developer--or a very up to date gamer--can answer that question. Of the two, the developer is probably the more accurate source if you can find a way to connect with 'him'.
So the answer to your question is "Maybe" but one can only be sure by asking someone who knows for sure and not someone who 'thinks' they know the answer--either the developer directly or by using one of the reliable available sources of information: forums, perhaps a google search, etc. and even then you may be wasting your money on a game that won't execute on your iMac. Just make sure you can return the game if it doesn't run. Of course, most game providers will not allow you to return an opened game so you might be unable to secure such a guarantee.