I don't know if you are interested in upgrading the PC a bit, but if you or someone you know is tech savvy enough, you also have that option. The graphics chip is probably the biggest show stopper.
The
HP Pavilion Slimline s3220n does have a PCIe x16 slot, so you could upgrade to an actual graphics card, instead of the rather weak integrated graphics you have now.
Even a cheap card of the current generation should help, or maybe someone you know has one lying around he/she doesn't need anymore.
A prerequisite is, that the power supply is sufficient for that and has the required connectors. If you don't know how to do all that though, let a professional do it.
Anyway, if you want to play the game, that's one more option you can consider.