The Playstation, at least, supports quads as a draw primitive. It does decompose these quads to tris for rasterization[1].

The Nintendo DS actually supports both tris and quads as rasterization primitives, which has some interesting consequences for shading[2].

[1] https://psx-spx.consoledev.net/graphicsprocessingunitgpu/#gp...

[2] https://melonds.kuribo64.net/comments.php?id=13