What's the integrated graphics platform, I/O, and CPU on the computer?
The GPU "acceleration" in Flash games is so dodgey (especially now that Adobe doesn't care about it anymore) that you're more likely getting hit by a CPU or even I/O bottleneck. Any DX10 capable graphics platform can acccelerate flash, whether it be a GeForce 8400GS or a GTX 690. (See:
GPUs supporting Adobe Flash 10.1) Something I learned recently from switch from an SSD back to a HDD was that the hard disk can cause what looks like frame skipping in a browser on Flash-heavy sites
(I soo hope my new SSD will arrive tomorrow!)
Do they happen to have 10 tabs (or malware toolbars) open when they play? Is the computer running a hard drive that's never been defragged in the 3 years you've owned the computer? If so, "there's yer problem!"