OpenGL, DirectX?
In DirectX, apart from swap chains, you can use view ports

In OpenGL, viewports are very trivial to set up and use. All you need to is provide the corner and dimensions to glViewport(), and then give the correct aspect ratio (width/height) when generating your perspective projection.

Just to clarify - viewports are not restricted to OGL/DX. "Viewport" is simply a term used to describe the use of cameras in a game scene. So you have a single scene that contains all of your objects, so in your case your scene would have the two bikes, your grid-like environment (arena) and any walls already created by the superbikes as they race around. That single scene can then be rendered from multiple angles with viewports. When you set the parameters for a viewport, you're deciding what the player can see from a certain location in the scene. So for split-screen, you have two viewports side by side rendering separate viewpoints of the scene. Just imagine it like those security camera monitors, the ones where you see 4 images on one screen, but they're all of the same room, just different angles.

Lol, did you play KH2? That was a good bike mini game.

that doesn't look too far off. This looks like a aspect ratio / fov problem. Check those values in the two projection matrices, they should be identical.