Stepper.h is really the Arduino stepper code so it is not likely to have many bugs. It could happen, but it is less likely that the problem is there.
That’s a very small stepper motor, so I would not expect it generate heavy torque. In the second video, he is using a 6.3V 175mA supply he says to get ~5V to the motor after the drop from the driver. He is running the motor very slowly at 3500us (3.5ms) per step. I think this might be the key to getting good results.
You are setting 120rpm and he says is using 8.4rpm. Have you tried slowing the motor down?