DMcG:
As I pointed out, no it doesn't. Losing a vote of no confidence would kick in a period of 14 days during which the Conservatives could propose some other person who commands the majority of the house. With the majority they have, that should be relatively easy. The only person guaranteed to lose their position would be Johnson.

That seems to answer your earlier question:
If anyone - Steve, Nigel or anyone else - can propose a way Labour could have called for any vote to remove Johnson that would be granted and binding, I'd be interested to hear it.