Yes, they have to pay him, but if I were representing ND in negotiating that contract, there would be a duty to mitigate (i.e. go find another job, in which event ND would only owe him the difference between what ND would have paid him and what he is receiving from his new employer) and a lump sum buyout at substantially less than full value, particularly when the termination occurred during the first half of the 10-year contract.
I'm assuming that mere losing was not grounds to terminate for cause. If it was, then ND owes him nothing. Of course, no coach in his right mind would ever agree to such a provision.