Eh, now we just getting into semantics.
While it is true that your monitor is 2-dimensional, when we say "3D" in the computer world, we are talking about how the game engine handles things code-wise. In a game like Wolfenstein 3D, DOOM, etc, everything you see is cleverly drawn sprites that look like they are drawn in 3D but they are always made to face the camera and only have a few different sprites that are swapped out as the sprite "turns" in relation to the viewer.
Environments are done by using vector graphics to draw lines towards a horizon point to give the 3D "illusion" and calculations are done on a 2D plane. Positions of actors (player, enemies, objects, terrain) are kept track of using two 2D planes, one vertical one horizontal (this is why such games almost always have flat floors, and no slopes, hills, etc).
In a true 3D game, the game's engine keeps track of things in three dimensions, with an X, Y and now Z coordinates instead of two X/Y axes. Calculations are done, characters and enemies are done using full 3 dimensional models that can be rotated in any direction and aren't just several different sprites that are drawn depending on which way they are facing, they are usually done by meshing graphics ontop of a wire figure, etc.
There's a huge difference in how these two different kinds of games work.