From the video, it looks like your motor is moving pretty well and you are fine-tuning. It is definitely possible that, as you mentioned, the issue is with the mechanical setup rather than the driver, but there are a few things we can check.
What is the current limit or Vref voltage of the driver set to? It does not look like you are stepping the motor very fast, but you can look at the pull out torque curve in the motor’s datasheet to get a general sense of how fast it can go with how much torque. If you compare your torque and speed to that graph and are close to the limit, you could experiment with increasing the motor voltage. If you have a scope with a current probe, you could also monitor the waveform of one coil and look for skipped steps.