A good $650 pre-built?

That's not a BAD computer if that's what you are asking. I would rather hand pick some other parts, but the 7770 is a pretty strong card and the FX-4100 isnt that bad. Seems like a decent build to me.

It doesn't come with a reliable power supply, so upgrades in the future might be limited unless that is upgraded by hand by the user. Overall, I would rather have a stronger CPU, but its still a pretty good build for $650
 
That's not too bad, you could do a lot better if you are able to build something yourself though.

For $50 less you could get something with a better CPU and PSU

Intel Core i3-2120
8GB Corsair XMS3 1333Mhz
ASRock H77M
Seagate Barracuda 500GB 7200RPM
XFX Double D HD 7770 1GB
Corsair CX-430 430W
Fractal Design Core 1000
DVD Burner

That would give slightly better gaming performance and should be more reliable at $50 less, total is $600 on Newegg.