Well, not merely in the sense that one might presume more money is involved in his work. But possibly in terms of the importance of those appointments to the patients, which is rightly a confidential private matter, so presumably yes, you shouldn’t bump doctors if you can avoid it…
Which gets back to how stupid it is for an airline to get to the point where they are forcibly bumping people. The PR impact of this one case is going to set UA back far more than they could gain by money-grubbing ovebook/bump tactics backed by stingy bump negotiations.
What seems even more significant about the passenger being a doctor, is that the three large young security guards had even less reasonable cause to regard the 69-year-old guy as a threat whom they should reasonably use injuring force on, and that UA staff should have been able to reason with him based on him presumably being an intelligent rational adult.
UA should train their crews in good negotiation skills, and give them enough authority to negotiate that they would never have gotten to the point of ordering random people off the plane.