Sorry, trying to dig through cobwebs of last time I worked on motors.
Yes, It looks like a permanent magnet DC motor, so the case holding the permanent magnets is the stator, and the windings are part of the rotor. As long as the case is fine, replacing the rotor (armature + commutator) and brushes is essentially replacing the whole motor.
Edit: that's not to say that something outside the motor couldn't actually be the problem. You could supply voltage directly to the wires connected to the brushes to verify that the motor itself doesn't run.
Further edit:
Jeremy Fielding on youtube has a good series on motor basics that I reference when I need a refresh. Here's a link to the first one.
https://www.youtube.com/watch?v=onjFFoOC_yk