You'd be surprised what you can run gaming-wise on just Intel HD graphics, an i3, and 4gigs of ram (and Win7 x64, of course). Nothing impressive (almost always low/lowmedium graphics for anything 3d and recent), or thats come out this or last year as a AAA title (indie games vary), but going all the way back ten years is a rather bad estimate, unless you're using a crappy integrated graphics.
Whether or not the game is optimized decently or not also is an important factor (ex. Magicka refuses to even startup on here, while TF2 works fine, Starfarer works great as long as it isn't a bajillion ships onscreen at once, Fallen Earth more-or-less works besides the current too many playeers in the starter areas problem, DDO looks quite decent on DX9, semi-low graphics mode, Sword of the Stars works great on the strategic map, only slightly slowed down on the combat map, a smallish fort in DF still runs at 500 FPS until either the fort or the population starts going uphill quickly, roguelikes of all kinds run as well as you'd expect, etc.)
Heck, I could run the Shogun 2 demo on this, though notably slower than I'd have liked and not at all as nice as the screenshots. Just takes some time, graphics setting restarts (start at either medium or low defaults, remove/minimize shadows, tinker a bit with the rest, and sometimes slightly less than full fullscreen). Need to not have much open at the same time as it besides Firefox & Steam though.