That's a phiddipus species, looks like, and you're right, those are its eyes. If you get it on the front of your monitor, their eyes are good enough that they'll chase your mouse pointer around. I've kept phiddipus audax before, and they're the coolest little spiders.

Thats nothing, lol, i have a tiny baby garden spider making a web on my moniter as a type... awww, he so ickle! the females can grow to the size of a pound coin.