Store Games on a Cloud and play locally?

Hey all,

I got my self a new Retina Macbook Pro, and while it's an amazing computer, the SSD is awfully small. I opted for the 256GB model but I may exchange it for the 512GB model next week, (PS, does anyone know how long I have to exchange, its been 7 days so far me). Anyway, I've always had low end macs like the white 08 MB and the 2011 MBA. I finally got my mac thats powerful enough to game. I play Diablo 3, COD 4 and maybe will download Starcraft II. Anyway, even if I get the 512GB model, I still would like all the space I can get, and if I stack up games, maybe even 512GB will start to strain.

Question: Does anyone know how to store games on a cloud (I know about Onlive but I'm not interested, I've used it) and log in a play them? I was thinking dropbox but I thought that maybe you would have to download the game once you wanted to start playing. Is there anyway I can store lets say Batman on a cloud, and one day log into the cloud and open the game and start playing?

Thanks!

Sorry but I'm cross-posting this throughout a few forums because I'm not sure what category this falls under.