Polygons have nothing to do with whether a game is 3D or not. You can have a 3D voxel based game. You can have a 3D super scaler sprite based game. Powerdrift actually has "floors above floors" even though it renders everything with sprites.
For context, when comparing the "3Dness" of a game engine, I'm referring to the ability to render objects in 3D space from different angles and perspectives. The less limited something is in terms of that rendering, the more "3D" it is.
I agree that the vast majority of games use various visual methods to convey a sense of 3D space. Even the use of parallax scrolling on platformers is meant to convey a sense of depth. In cases of 2D sprite based games such methods are primarily illusionary. We're not dealing with proper 3D geometry.
Taking something like Powerdrift, it uses sprite scaling to convey a sense of 3D. But it's limited. For example, if I wanted to render an overhead view of the track instead... well, I couldn't. The only way to create such a view would be to have an artist create a whole new set of sprites and then reprogram the game for that POV.
Doom is more advanced, but it still has similar limitations. It is just a projection of a 2D map with sector heights and clever rendering to give the illusion of 3D space. But there is still a lot missing in Doom. For example, when we talk about rooms-above-rooms, we're really talking about the ability for the engine to render planar surfaces above each other. In the case of Doom it can render a floor and a ceiling, but that's it. In absence of those it renders a flat 2D background to create the illusion of an outside world and buildings within that world. Yet those buildings that you can go inside don't have roofs. You could never look down on the tops of those buildings. The Doom engine cannot render that perspective.
When it comes to try 3D polygonal geometry, it's generally possible to render it from any angle and perspective. Such is the case in Starfox which even the simple flyby level introduction demonstrates. Likewise there are 3D polygonal objects in Starfox that for all their simplicity would be impossible to render in the Doom engine. And no doubt Starfox employs its share of pseudo-3D trickery as well, such as on the planet levels using flat backdrops to convey a sense of a world (same as Doom does). But Starfox still employs 3D objects not capable of being rendered in something like Doom.
In theory in world of unlimited performance, the underlying engine/code-base used for Starfox should be capable to creating the 3D geometry for a game like Doom. But the reverse simply isn't true, because the way the Doom engine is build prohibits the type of geometry used in Starfox.
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