Besides monitoring voltage via the MB temp sensors (inaccurate), you could check them via a multimeter... but quality of the power is much harder to measure (without thousands of dollars worth of equipment).
Have you considered the problem possibly being the gateway logo on the front... hehe, just joking. My advice would be to complain until they send you a new box. OEM computers aren't built for performance as much as compatability. The problem could be anything from the power supply, to the mobo, to the memory, or all three. Even though the problem only comes out in games, it should have been found in a burn-in test.
But before that you might as well try to upgrade the BIOS, the video card drivers, the mobo chipset drivers (if available), and the sound drivers to see if that helps. You could also try to disconnect any non-essential parts from the system (ie. sound card, addon-cards, extra HD's, CD/DVD, usb devices), and try running the games to see if they're fine with less power draw, which would single out the power supply.
