I define "moderate gaming" as actual 3D gaming (games like L4D2, Sim City, Portal2) not casual games. In which case no. Most of those PCs have on board Intel video which sucks for gaming. A modern Intel video chip is okay for moderate gaming, but 3 or 4 years ago (about the age of those refurbs) Intel was useless for gaming.
You could always install a decent $100 gaming video card in one of the full towers, and as long as it's at least a Core 2 Duo CPU you'd have a low-end gaming rig. However you'd end up paying almost as much for a NEW low-end Core i3 system.
Instead I would shop around for a deal on a new Core i3 or Core i5 desktop. A lot of OEMs are going to be retiring models with the last generation CPUs.
Some good prices on new Dell Inspiron 660. Base price of $429 for a Core i3 and it comes with Win7:
http://www.dell.com/us/business/p/inspiron-660/fs
Here's the service manual for the Inspiron 660 if you want to see what it looks like inside: [url]ftp://ftp.dell.com/Manuals/all-products/esuprt_desktop/esuprt_inspiron_desktop/inspiron-660_Owner%27s%20Manual_en-us.pdf[/url]
He can maybe save up to upgrade the video card later. Just make sure that there's a PCI-E x16 slot in whatever he buys.
He can also keep an eye out for deals here:
http://dealnews.com/c48/Computers/Desktops/
A Core i5 is going to be better than a Core i3, and better onboard graphics as well. They are usually priced $100 apart and a Core i5 is usually around $500.
Just make sure to stick to a full tower. As long as it has a PCI-E slot and a standard PSU, the video can be upgraded later if he wants more gaming performance out of it.