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 hold to my definition that if the 3rd dimension affects gameplay, it is counted as half a dimension if the rendering technique used is not full polygonal 3D.
Though it definitely is connected to the visualisation you choose to use.
Sim City 2k graphics is 2D, and the "emulation" of depth is achieved by isometric techniques.
If you would add terrain height change to any 2D game, you would need some way to show that the terrain height change had happened.
If you do this with some graphical effect, like some shading, a scaling, fog, etc, that give some illusion of depth, the game would then become a 2.5D game.
If you just have a number "5m above ocean" on every tile, then it remains a 2D game.
Yes, it seems that to many, a game being 2D, "2.5D" or 3D is directly connected to how it's rendered.
Personally, I wouldn't say using or not using polygons should have any impact to whether a game can be considered 3D or not.
A heightmap is a good example of something 2D which just as easily represents something 3D. The third dimension being the intensity of each pixel.
Had I been comfortable with viewing a heightmap myself, while playing an otherwise 2D rendered game, its mechanisms could be just as 3D as Simcity 2000.
Changing the terrain would be nothing more than altering these values, and if my brain decides to view and understand the heightmap as being 3D, then I percieve the game as 3D. (I may use bump-mapping or similar, but it won't be a fancy projection)
It always ends up as 2D, and it's up to us to have the users perceive depth, if we want them to.
I'd say that the text "5m above ocean" displayed on a tile is just as clear an indication of 3D as a heightmapped terrain.
I completely agree that you can, and should, fool the user into seeing 3D, even with the effects you mentioned, but I think the idea of 2.5D is very vague.