Now here is an example of a distinction without a difference.
Nixon had 2 1/2 years to go on his term–the executive in charge of the oversight of the entire Federal government. Watts had six months left, most of it scheduled for summer, pre-election, and post-election recess. He had also achieved the number three position in his party in the House, thus, regardless whether he is (objectively or in his mind) being denied the ability to wield that power, he has certainly declared his intention to walk away from it. In addition, before he announced that he would not run again, he was considered to have pretty much a lock on his seat–which, again, his is giving up.
If you wish to define quit so narrowly as to mean only “immediate surrender,” I suppose you may. Given that most people recognize that the job was “his” for the foreseeable future, an announcement to not run is tantamount to an announcement to quit.