Thank you for both answers, they have pointed me in the right directions!
It seems both solutions are used: for better, more precise (and expensive) controllers current sensing is used. Cheaper controllers seem to use PWM only. I suppose my wheel was one of the cheaper ones.
I want to use the motor, as I already have it assembled - only the board is faulty, the mechanics remain the same. Besides, I am somewhat used to the feel...
If I understand it correctly, to obtain resistance, I have to sense the direction of the rotation and counter it with the appropriate torque? Or is the braking force of the H-bridge sufficient for that?
One more question: I have no idea how much current the motor might take. Would the power supply nominal values (output 24V, 0.75A) be sufficient to determine that?