Lets look at the specs of pc against Starcraft 2 recommended requirements .
CPU : Dual-Core 2.4Ghz, HP has i3-530 Dual-Core@ 2.9Ghz - OK
Memory : 2GB, HP has 6GB - OK
Video : GeForce 8800GTX or ATI 3870, HP has Integrated Intel HD - RUBBISH, You can install a PCI-E x16 video card, but PSU wouldn't handle it.
O/S : Vista / Windows 7, HP has Windows 7 Home Premium x64 - OK
My personal feelings, never buy a PC that comes with onboard video if you plan on gaming. 99% of the time, you will have to splash out £££ later on.