Briggs and Stratton 123K02-0454-E1 Choke Not Closing?

I'm visiting my daughter's family in Virginia, and volunteered to repair their Craftsman push mower (model no. 917.387681).  Problem: Starts right up, but dies after a couple of seconds.
 
Looks like the choke is not closing.  Discussion here and there says these engines, or some of them, have thermostatic-controlled automatic chokes. Not sure if this one does, though.  What I thought was the choke seems to be a throttle plate, held open by a spring.  Is that the choke.  The lever on the other side of the engine pivots on a bolt going inside the engine body, not an independent thermostat.  So I am confused.
 
Is the spring-controlled moveable plate the coke or a throttle plate?  Is the lever a thermostat, or a governor?
 
Can't see to find good diagrams or photos or videos of this particular model no., even here on Jack's.
 
What am I missing?
 
Engine model: Briggs and Stratton 123K02-0454-E1
 
/Mr Lynn