Isn't this exactly the world that free speech / pro-liberty advocates want?
I don't have any power to fire someone from their job; I'm not their boss. But I do have the right to make my views about them freely known. That's my right to free speech. And I can also decide whether to patronize their business or not. That's my right to economic freedom - to not be in an authoritarian society where the government tells me what I have to spend my money on. And their boss has the right to decide whether to employ them or not. That's the boss's economic freedom and at-will employment.
If I'm threatening the boss with physical harm (violating the NAP, as some would say), then I'm clearly in the wrong. But if I'm making my opinion known, and their boss agrees, isn't that the intended effect of discourse? What is the point of free speech if there isn't the possibility that people might be influenced by listening to that speech?
I don't see any way to cancel Twitter mobs that doesn't itself uphold cancel culture and destroy liberty.
(In any case, in the article at hand, "Twitter mobs" isn't a fully accurate descriptor. The quoted tweet was from an alum. The ability for alumni to contact their university and make their opinions known - and have their opinions be taken with more weight than those of the general public - has existed long before Twitter and will exist long after.)