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> I think it would require one eye above the other to have depth perception in his 2d world.

Is his world actually 2D though? Or a 3D world projected down to 2D? The latter is what I would expect.

The specific restrictions on his movement would seem oddly coincidental if he’s in fact in a 3D world that we just happen to be seeing projected in 2D.

He can move behind some objects though, such as flags, which indicates there is more than one pixel width in that plane.

This does not work with going down the pipes, since he disappears "into" the pipe (so behind the front part of the pipe)

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