For me this seems a nice deal, but im no laptop pro...
yes this system should run games without a problem you have a nice GPU and a pretty nice CPU for laptops, however for this much you could have bought it brand new [if it isnt...]
About 'how much I have space you actually left with ..."
to begin with take 4.2 GiB [Following this post
in the bottom of that post you can read about the true amount of bytes within a GiB]
So you actualy have 55.8 GiB in it, then take off like 2GiB just for the windows [so I remember it is..] and programs would sum up for another 2GiB [if you'r a standard user] thats another 4GiB, so.. 51.8GiB +/- left....... games, videos, etc.. you know what you have for the rest, lol.
Well anyway I'd suggest you get a better HD because 5.4k RPM is pretty low for nowdays..
I still think this is a fine computer for an OK price.