The entire cube gets clipped away, I guess we're just very slightly off from what the real PSP is doing.
The reason this is happening is that there's a digit missing in the projection matrix, causing it to squish the cube flat against the Z=0 plane, so this cube will not depth test properly against anything else. The perspective projected texturing still works (if you pass the clipping) since the W coordinate is computed correctly.
Note how the third row (actually column, I believe, but viewed transposed) of the matrix is 0.0f. There should be at least one non-zero number in there.
I'm aware this project isn't maintained now but I figured I'd track this bug in the project anyway incase someone else wanted to resolve it.
Details here: https://github.com/hrydgard/ppsspp/issues/17981#issuecomment-1851025066