I am not even remotely a lawyer or qualified to actually answer this, but my guess is the situation here didn't actually prevent United from fulfilling their contracts. They just chose to ignore their contracts because they thought they could get away with it.

Force majeure doesn't apply in this circumstance because it requires an external force or event that is unforeseeable. In this case, United didn't plan correctly for the transport of its 4 employees, something well within its capability to predict.

It's possible that United did plan correctly for the transport of those employees, but the employees themselves failed to follow the plan. How was it that the 3411 crew didn't even know the other crew was coming, until the very last minute? That's extremely unlikely if the other crew had been scheduled for 3411. It's more likely that they had originally been scheduled for another flight, missed it, and got to 3411 before word did (possibly because of poor communication between United and Republic). At the very best, they were later than they should have been. Why? And did they (or someone else) pressure the 3411 crew into doing what they did?

United still screwed up in a lot of ways. So did Republic. So most of all did the aviation "police" - an organization that seems to consist largely of people thrown out of CPD for exactly the kind of misconduct visible on the video. But somewhere in there I think there's a fourth group that screwed up - the people whose sudden appearance triggered the whole mess.

There were massive storms in the few days prior to the incident. That could disrupt their planning.