I think saying 2.5D has become a way to describe what a game feels like without actually taking the time to say how it works.
Ultimately, in graphics, our games end up being shown 2D. How they get there is, even today, perspective or ortographic projections.
Billboards and 3D meshes. The bar for how much it takes on the graphics side to be qualified as 3D is probably changing, although I still regard Wolfenstein 3D as being a 3D game. It has what appears as perspective, and in a way, that's enough to describe 3D graphics it for me.
Its gameplay mechanisms are pure 2D, though. Simcity 2000 and up are regarded "2.5D" by some. Sure, a change in terrain height can mean higher land values, but you could emulate that in 2D as well. I like to work in integers when describing D. I cannot imagine half a time axis, or half a color or geometry axis. It's just plain silly, or maybe I'm not bright enough. I'd say simcity could just as well be shown/understood as a 2D game with 2D visuals.
Everything can be spoken of in as many D as you like, only after a certain count it stops making sense to me. I have this tile which travels in time. Now, it's condition dimension is 100%. It's ownership dimension is 1, for player 1. It's temerature dimensions is 20 deg celcius. Oh, and it has X and Y coordinates too, but I'm somehow still able to describe it as a line on graph, with alternating thickness, transparency and rgb values.
If it makes sense to you, go ahead and use that half dimension, -but please try to explain where I can find this dimension, and how it's actually represented in the game.
I'd still say that if it makes sense to have an altitude for objects, the game would be 3D from a geometric point of view, not 2D, even though the isometric projection results in a 2D image. All the projections I work with in GD do.
The guys on the wikipedia article seem to be all over the place. Where I'd say 2.5D doesn't mean anything really, these people apparently have a lot of opinions on the subject, changing from describing projection types and gameplay, to talking about parallax scrolling, 2D gloss effects and bump mapping. It's probably safe to say that they're not completely sure either, although overall it seems to have something to do with pseudo 3D, and making things appear to have more depth when shown in the plane.
I've never come over a paper that describes an improvement to creating lifelike geometry as "improving 2.5D graphics" or "for applications in a 2.5D environment"