I have no problem with a blockchain used in non-monetary context. Consider, for example, a competitive RTS/TBS which recorded RNG events or keystrokes to the blockchain, which helps show if there was lag, and helps to verify that the RNG is fair, and that both players aren't cheating. Or a game with a "Speedrun" mode, recording input as blocks, and making sure it's all publicly verifiable. Think of a Doom demo file, but encompassing all attempts from all connected players; new routes can be discovered quicker and cheaters can be outed near-instantly.

Blockchain as a concept is of great value to anything where public auditing is wanted. We've associated it to scams and money, and that bugs me. Including more aggressive monetization, speculation, and a profit motive makes a game less fun. Including a publicly auditable log of past events in a game built for multiplayer feels like it would be a value-add.