The design on earlier ones, and I think this one, is for the throttle linkage to turn the lever at the fuel pump to zero fuel. Try reaching in and doing that. Then adjust the linkage, or foot throttle, so the linkage can reach zero.
I added a screen door spring on one tractor to pull the worn linkage the last bit to zero, an impatient temporary fix to get through the day until I could align the linkage back to spec.
Some tractors have a 'pull to stop' lever or a solenoid, that shuts off fuel. Not the old Yanmars. And the key does nothing. It's only for cranking the engine, and allowing the charging circuit and lighting circuit to be connected.
The compression release is for cranking it before starting. It can be used as an emergency shutdown but that's not recommended, its components aren't designed to withstand a running engine.