An easy tell is walking up to a painting or even looking at the pillars you see from your starting position: you'll notice that the vertical lines aren't perfec

An easy tell is walking up to a painting or even looking at the pillars you see from your starting position: you'll notice that the vertical lines aren't perfectly perpendicular to the horizontal lines in screen space, because the camera is pointed slightly upwards. In Doom, walls are rendered as strips of screen columns, and the pitch of the camera angle looks like it's perfectly parallel to the horizontal plane as a result. You can sort of implement looking up and down with minor modifications to the Doom engine, and this was implemented in Heretic, but because of the nature of the renderer, vertical lines in the world remain vertical lines in screen space even when you pitch the camera, so it looks somewhat distorted in a way that's very characteristic of the post-Doom "2.5D" engines.