I did read his code, did you?
Here's the relevant parts,
DCMotor m1(5,3);
DCMotor m2(11,9);
m1.run(speed);
m2.run(speed);
He feeds this value into the motor controller, that simply linearly converts it to some PWM output to drive the motors.
It's not linear, there is a control loop on the current.
"The MC33926 works with 3 – 5 V logic levels, supports ultrasonic (up to 20 kHz) PWM, and features current feedback".
There is a physical model behind it, you're just choosing to ignore it by 'tweaking' the PID with trial and error instead of actually doing the calculations. It would take less than an hour to build a physical model, find the differential equations(Also available on wiki), find the PID gains with Root Locust or any other method. It's a very common homework assignment given to students(My self included).
With the exception of some remote control code, that is ALL his code does.
You're right about that.
Again, all I'm trying to say is that the motor controller handles the torque control for him. This is why most projects like it use an encoder or a motor controller, using just an H-brdige and PWM probably won't work well.