I'm going to guess that the fuel circuit on the Yanmar engine in that Deere 750 is near identical to my Yanmar engine in my Yanmar 240. (approximately the same year model). There is no solenoid, no electric fuel pump, no pull cable, or ignition (obviously - it's a diesel).
The throttle lever simply controls how much fuel the injector pump puts out. You pull the throttle down to zero, the pump output is zero, > the engine stops. It's just that simple.
The key is completely unrelated. It controls the starter motor, the manifold heater, and engages or disengages the charging circuit. Turning it off with the engine running has no effect on the diesel engine, aside from the battery is no longer receiving a charge.
Recently I turned the key off and pulled out the key to use the knife that is on my keychain - with the engine still running. When I put the key back in a moment later I forgot to turn the 'ignition' on and ran the rest of the day with it at 'off' position, only discovering my error at the end of the day. The engine never knew the difference. (I've read that doing this might damage the alternator, but it didn't in my case).