Yes, a processor is required. My 2011 middle-of-the-road laptop can just about cope. But to err on the side of caution and also try to sound a little less clueless about hardware, I'll say an Intel i3 or better is probably wise.
You don't need a beast - as mentioned above, my ancient laptop (it's called Larry, by the way) has something known as a Radeon HD 6520G stuffed inside it, and it can just about deliver 30fps with all the settings on "Low". Definitely wouldn't want to go older/lamer than that, but the fact you're actually looking at 3-dimensional games on Steam makes me think you've probably already got that covered.