I assume they're trying to state that the force from the motor torque (N or lbs) times the radius is equal to the weight force (again N or lbs) times the radius.

This equation might better be stated as:

r x F = r x F

If you are using spec motor torque from a sheet, the units would be in N-m or lb-ft (or some derivative of those two) and would be equal to r x F (meters or feet times newtons or lbs)

The motor torque is:

T = r x F

Motor torque in those equations is a force not a torque, so you are correct.