We used to
have to put "motor run" capacitors on all our
large equipment (3 phase) to get our power factor closer
to one (unity). However, this system is a single phase
system. I don't think the same issue is being addressed
by the run capacitor.
It is, like the capacitor in flourescent light fittings the
run capacitor on a motor is (usually) just for power factor
correction and it matters not if it's 3 phase or single. The
give away is if it's across the supply or in series with a
separate winding. If it's across the supply then it's for PFC.
The drawing does look as though it is in series with a second winding.
Vince