Perhaps this implementation works that way, but in principle if the game is strictly determined based on a random seed and player input, then the server can verify that the player's inputs do in fact result in the correct outcome.
…hang on, this is starting to feel like Elliptic Curve cryptography: it’s trivial to prove a demo file is a “solution” to a random-seeded Doom map, but nontrivial to work-backwards to generate a demo-recording.
The heart of Bitcoin is just "Find me a number between 0xf80000 and 0xff0000 whose SHA-1 hash starts with eight zeroes..."