If it helps, think of it as an “actual 3D” scene where objects are laid out in three dimension, but within each bounding box is just a 2D painting of that object. So wherever objects intersect they just act like flat sprites hitting each other. They also have flat (2D) lighting.
It’s very similar to a sprite based 3D engine.
For other “pseudo-3D” engines see Wolfenstein, or even Super Mario which has “actual 3D” parallax but 2D drawing within each layer.
Another example is Heretic (a Doom engine variant) which could fake looking up and down by warping tiles, but distortion increased the higher up you look.
In every case there really is real 3D projection. But it just doesn’t go all the way. It retains some 2D algorithms for some part of the rendering.
Sadly, 2.5D has basically lost all its meaning. It's sometimes meant to represent sidescrollers that use 3D polygons, or even fully 3D games that just have a certain camera angle, or any number of other things. :(
Heretic is a 3D game, as was Doom, since the world is really 3D: in addition to the 2D vectors making up the walldefs, there is a height component in each sector and entity which adds the third dimension. That some parts of the game (entity-to-entity collision, but not hitscan-to-entity which knows about elevation) ignore the 3rd dimension or that the renderer took advantage of the way the world was represented to speed up wall rendering doesn't really change that the world itself is made up of three dimensions.
Entities being 2D sprites is also irrelevant as they are just billboards and many engines even today use billboards for various reasons (particles, foliage, LOD, etc). They are also placed in 3D space.
Wolfenstein 3D on the other hand, yes, that is a fully 2D game as there is no third dimension outside the implied wall height used during rendering.
I mean, it is really simple, there isn't need to justify some old misconceptions about "2.5D" or whatever that persist due to pop culture: if your graphics data has three dimensions, you are doing 3D graphics.
This is an element of how rasterization is performed and has no implication on if graphics are 3D or not though. PS1 hardware having no perspective correct texture mapping doesn't make the games that used it "not 3D" - and on the flip side, a side scrolling 2D platformer using a rasterizer capable of perspective correct texture mapping (like any platformer that uses OpenGL or Direct3D to render its worlds as triangles) doesn't make the game use 3D graphics.
It’s very similar to a sprite based 3D engine.
For other “pseudo-3D” engines see Wolfenstein, or even Super Mario which has “actual 3D” parallax but 2D drawing within each layer.
Another example is Heretic (a Doom engine variant) which could fake looking up and down by warping tiles, but distortion increased the higher up you look.
In every case there really is real 3D projection. But it just doesn’t go all the way. It retains some 2D algorithms for some part of the rendering.