The actual process of doing it is possible; people load things onto USB sticks all of the time (programs and whatnot, not just files). The problem is, as many have stated here, is the speed you're going to get.
The flash storage in SSDs is different in that the read/write speeds are fast. Very fast. I used to wonder (when they first came out and I didn't know anything about them) why people couldn't just throw some 32gb micro sd cards in there and have the same result.
You could store the game's files and whatnot on there, then copy/move them to the computer if you want to do that, however I doubt you'd be able to game from that drive.
Now you "might" be able to do it with a thunderbolt port and a supported drive as the speeds might be a lot faster with that. External SSD drive to thunderbolt maybe?