I must admit that I'm no longer sure what we're debating. But here's a reflection of my current understanding.
The original motors do not have an analog tacho, but they do have a digital incremental encoder. The drive hardware appears to be an open-loop H bridge that is PWM controlled. The motor encoder does not connect to the drive hardware, but it did connect to the original microcontroller-based control unit.
Other than when stopped, the open loop drive hardware seems to act like a velocity drive. Commanded PWM value correlates to speed, not torque. It is not commanding the drive to output a current, it's commanding the drive to output a voltage.
When stopped with a 0 PWM command, it does appear to be a bit like a torque drive in that the shaft can be rotated (though there is some resistance as you try to spin it quickly).
However, in the original system, there was a control loop running on the microcontroller that took take the place of the tacho feedback in your drawing, and if it "saw" motor encoder movement when stopped, it would command a PWM value to try to maintain the zero position. And likewise when moving, it could more closely control the rotational speed to the commanded value by monitoring the encoder in the control loop.
If my understanding is correct, as a system, the original inner loop probably acted like a proper velocity drive, but the feedback was implemented with a digital encoder and a control loop in firmware instead of with analog tachos and op amps. If we focus on just the hardware portion of the drive as we have been, it's really not exactly a velocity drive (but it is similar), nor is it a torque drive (except it kind of looks like one when commanded to stop).