I keep reading these references to Doom 1 and other 'first generation first-person shotters' as being "2.5D" To me this somehow implies they are 3-D perspective, but not quite up to today's "true 3-D" ...

2.5D platformers offer a unique combination of 2D gameplay in a 3D space. Some of the best games in the genre incorporate the 2.5D perspective into gameplay, with hazards striking from the background.