The demo you are watching is an agent trained from scratch with reinforcement learning. It has roughly 6 days of experience (10M steps at 20 Hz). The Javascript demo is replaying the policy open loop which is why it's not super robust to disturbances.
Re:fingering: we actually use fingering information to create a dense reward for the agent (otherwise it makes exploration super hard). It would be an exciting future direction to have the agent discover and optimize for fingering that best suits its kinematics :) And beyond that, having RL inform pianists about the difficulty of a piece or even more optimal fingering would be amazing.
We trained a bunch of these policies on roughly 150 songs (baroque, romantic, classical) and we did some analysis in the paper if you're interested: https://kzakka.com/robopianist/robopianist.pdf