Afaik, the GTX 645 will easily beat the 7570 on any task. Has around double the specs and double the points in all benchmarks. As of here.
By eyeballing from the benchmark scores it should be able to handle anything relatively new/demanding as long as you don't put details to more than medium and don't run a TV or more than 2 screens with it. With older/less demanding stuff as the games you cited it will likely yawn at any resolution.
What about purchasing just a cheapo card for 50 bucks and place it in the HP PC? Given her selection of games upgrading the whole PC and getting one with a i7 4770 is beyond overkill.
All arcade-like games are a piece of cake even for the i7 4770's integrated graphics (the HD4600).
Heck, Luxor HD is available even on friggin iPads (that run it in HD). It's not anywhere near demanding.
What's the specs of the HP PC you have? Does it have a PCI-express x16 slot? (post the model if you don't know) this tutorial
has a tool that scans and tells the specs automatically.