Hard Relay Mario Brothers is a sadistic hack of Super Mario Brothers that requires players to exploit glitches to complete the game. While an emulator is used, it still takes skill to do tricks like bouncing off a moving koopa shell and passing through solid objects. TAS videos explains how to do some of the feats like the first trick seen in the video, the walljump.
Theory: Walljump happens because the game does a floor check (a simple "is position divided by 16 even? Is there a solid block below him?" test) even during a wall-ejection. Wall-ejection is SMB’s mechanism to adjust Mario’s horizontal position properly when his left side and right side have a different inside-wall status. The game ejects Mario towards the opposite of his steering.
To perform a walljump, you need two things:
Some horizontal speed (towards the wall)
Mario’s feet must hit the wall exactly at a block boundary (every 16 pixels)