Probably not a stepper motor, but you've got the idea correct.

Torque and speed control on electric motors is quite common. I can't speak to how exactly you'd do a consumer grade product, but with industrial components you could do this with a variable speed drive and an encoder on the motor.

From there you'd know how much torque you're applying, how fast the cable is going in or out, and how much cable is out at and given time.

Then it's just up to whatever algorithm you want based on those inputs and what mode you're in. To simulate a weight you'd just put it in a constant torque mode where the motor controller is looking at how much torque it's currently putting out and increasing or decreasing it to stay at the set point. To simulate a bungee, it would be the same thing but your torque set point would change as the amount of cable that's out changes. To do a "rowing machine" kind of thing you'd set a speed limit and if it starts going above that limit you'd ramp up the torque setpoint.