In some video games, they would just model the mirror image of the room to cheaply get a mirror to look correct. Some hacks would allow you to walk into the mirror world.
Otherwise, it's normally done with a clipped modified camera projection and rendering the original scene.
All in all it's a lot more complicated than you might imagine.
The mirror in Duke Nukem 3D blew my mind a little bit as a kid and was the first one I saw in a game, and I assume must have been made like that.
It gets even weirder when there's a room behind the mirror that you include in the photogrammetry scan