AB2012: I think there's a general tendency particular for those of us over the age of 30 to equate "old games" with "only 1990's stuff I grew up with". As you said, 2006-2012 games are just as old today as many 90's games were by the early to mid-2000's, even though people don't see them as the "same kind of old".
There was, at some point, a major shift in the way games were designed and developed. Here are some shifts that have occurred at different points:
*: The use of 3D graphics hardware. (I like to use this as a rough point to distinguish old games and modern games)
*: The use of CD-ROMs for storage of game data (before then, we only had floppies or cartridges; before that, games were stored on cassette tapes)
*: Shifts in genres and genre conventions. For example, in the late 90s, you stopped seeing turn-based WRPGs, and JRPGs started having lots of FMV and minigames, as well as the standard JRPG party size shrinking from 4 to 3.
*: Related to the above: Endangered/Extinct genres. Text adventures stopped appearing a long time ago, and there was a while when 2D platformers became extremely rare, especially on home consoles (the SNES had far more 2D platformers than the Nintendo 64, for example).
(In case you haven't noticed, many of the changes I mentioned above actually occurred around the same time, although I believe PCs got CD-ROM games earlier.)