It's not getting anything, it's providing a slur so the 2 hot legs have somewhere to go to flow power through them: it's a cobble Band-Aid to make a 3ph motor spin with a missing leg and 180 degree phase shift input. You need a start capacitor just to get the phases out of phase enough to buck each other. Without that, you get jack-spit at the armature.
Think of it like this: single phase = you have 2 guys pushing/pulling on a car that's stuck in the mud, but they're each throttling their effort in perfect harmony (180 degrees out of phase from each other). One guy pushes the other guy pulls at exactly opposite potentials. The car doesn't move!
Well, we can't get anything done with that kind of effort, so we're going to trick one of them into pushing and pulling slightly out of sync with the other one (this is what a starting capacitor does) and now all of a sudden we don't have systematic paralysis, and that little difference in forces allows us to move our car enough for the tires to hit traction and now the car gets itself moving. That's how a 1Ph motor works.
With 3ph we have 3 guys, but they're on different corners of the car pushing at 120 degrees to one another. As one pushes his hardest, the guy next to him is starting to throttle up and the other guy is starting to throttle down, but two of them are pushing at the same time all the time. This is why there's no starting or run capacitors on 3ph motors - they don't need them to create a bucking current to start the motor.
That you can delay the wave rise and fall enough to make a 3ph motor spin on 1ph is not an accomplishment, it's a detriment. You will overload the two winding's you're using and the third one has ZERO input. We had 3 legs with equal power inputs, now down to 2, and without that capacitor they're working 100% against each other to keep your motor turning. As you load that motor down, you lose more and more of your available power until it stalls. With a 3ph motor, as you load it down, it draws more and more current fighting to kick the car out of the mud.