"I don't know, but I think it is likely that the use of the word 'resign' is somewhat fluid here (not by you Friday) in which case it is likely that the payment to end of contract is in lieu of notice which is what grown up companies do!"
They had grounds to sack her for cause: she presided over an organisation which paid out millions of pounds without authorisation, what grown-ups call "theft" and "corruption". Even if they had terminated her contract without going to the lengths of actually dismissing her immediately, they could have announced "her contract has been terminated as the BBC no longer has confidence in her", paid her off and escorted her off the premises (as she would have done to others).
Instead, she gets a laudatory send off, the pretence that she's a great loss to the organisation, her contract paid in full and (pace those questioning the use of the word "payoff") let's wait until she's actually gone to see if she gets something extra for the journey: if she doesn't, she'll be the first BBC executive in living memory not to.
In BBC-land, you can resign from your job, take another, and still find yourself in receipt of £375 000 of completely non-contractual wonga, just for being a nice chap. That's, what, a couple of thousand annual license fees? Sure, Keating is said to have given the money back, but that's hardly the point, even if it's true.