For those of you who may not know, Alternity is a sci-fi roleplaying system released back in 1998 by TSR, the company that, at that time, also owned D&D. It was discontinued two short years later and many of the ideas therein were brought over into d20 Modern in 2002. It shares many mechanics in common with D&D 3.5, which you may recall these ladies were playing a few short weeks ago.
Although Alternity comes with its own setting - aliens and mutants and such - it was designed to be a generic roleplaying system that can work with any sci-fi setting, and Lily uses it as such.
The idea of roleplaying games being old or outdated is an odd one. On the one hand, they certainly don't go bad over time - Alternity is certainly as playable now as it ever was, and it's not like console video games where there are obvious differences in terms of graphics quality. On the other hand, though, I do think that tabletop gaming culture has advanced and that new ideas have come along that make newer games better (and certainly more accessible) than older ones were. I would definitely prefer playing 3.5 or Pathfinder to the original Dungeons and Dragons, and I expect and hope that future generations will prefer playing newer games to 3.5 or Pathfinder.
Now that I think of it, it's sort of weird that the hobby as we know it only started in the mid-seventies. One wonders what tabletop roleplaying games and their associated culture would look like if they'd first become popular during the Great Depression, or in Victorian England, or in Ancient Rome. Perhaps, by now, they'd have accumulated a veneer of class and sophistication. Perhaps museums would display busts of great game masters from ages past. Perhaps the tabletop gaming industry would be comparable to (if not larger than) Hollywood.
Perhaps, by now, someone would have figured out a decent mechanic for grappling.