I thought of that idea with the engine needing to turn to release the pin, but like you noticed, that one has a large delay that can't be explained that way.
I thought they all had a longer delay like in the video above, but after studying two other videos of a startomatic starting, it looks like the pin must be held in place by the force from the valve springs. I wouldn't have guessed that would be enough time for it to spin up and actually make it past compression. I guess it is though.
The controlling circuit that I'm making does use delay relays. They control the glow plug, starter solenoid, fuel control solenoid, the overload alarm and the overload shut down system.