I know you probably don't want to hear it, because you're looking at stock PCs but honestly the best option is to build your own.
Building a PC takes ~3 hours when you're a complete noob and is really pretty easy. The motherboard comes with instructions and most stuff that isn't supposed to go together doesn't fit anyway. No soldering (I saw someone ask this once) or anything crazy required.
If shopping for parts intimidates you or you don't have the time there's this thread:
best PC for $500
most posts explain the strengths and weaknesses of their builds as well.
To answer your question though, no. I don't think the graphics card is good enough to run modern games well. Though I may be wrong... they don't have a lot of info in the specs section for it.