This one says "Standard or high force push switch option" so I assume this is intended to be a switch on a panel...
Yes, it's for use on instruments and the like and the push switch is just to give you an extra control in the same form factor - one likely use of it would be to switch between 2 (or more) increment modifiers, making it able to go in steps of eg. 1 and 10.
Maybe this isn't the right kind of encoder? Is there some kind that is intended for use as motor feedback? I assume I could make it work anyway...
It isn't the right one for motor feedback. You could make it work of course, but it would be a poor solution. It has a max. RPM of 120 and the rotational life at 30 RPM and it's torque that will load the motor is not very impressive in a motor feedback, to put it mildly.
This is a very fine (mechanical) device for the intended purposes, but for motor feedback, you want "eternal" life and zero drag.
A slotted disc and 2 pairs of IR emitter/receiver (2 slotted opto couplers or reflective switches) is what you need, just like in an old school ball operated mouse.
If you only need speed and not quadrature (for rotational direction), one opto-switch is enough.