It will probably run but I doubt you'll be happy with the perfromance
of the UMA 945G chipset running games.

I'd suggest that you get the newer HP Slimline s3000y (Intel) or
s3000e (AMD) and configure it to order on hp.com where you can add a
graphics card.

For instance this might be a good config for your needs:
Operating System Genuine Windows Vista(TM) Home Premium
edit
Processor Intel(R) Core(TM) 2 Duo processor E6300 (1.86GHz)
edit
Memory 2GB DDR2-533MHz SDRAM (2x1024)         edit
Hard Drive 160GB 7200 rpm SATA 3Gb/s hard drive         edit
Primary CD/DVD Drive LightScribe 16X DVD+/-R/RW SuperMulti
drive         edit
Graphics Card 256MB NVIDIA GeForce 7500LE         edit
Sound Card Integrated 7.1 channel sound w/front audio ports
edit
Front Productivity Ports 15-in-1 memory card reader, USB, headphone
port         edit
Keyboard and Mouse HP keyboard and HP scroller mouse         edit
Productivity Software Microsoft(R) Works 8.0         edit
TV & Entertainment Experience No TV Tuner w/remote control
edit
Networking No modem and no wireless         edit

Ken