Of course he is (if he ever was in the first place).
He just can't be "elected" President again (and as I have posted elsewhere, that really depends on what XXII means by "elected").
It’s fairly clear that the Electors meeting in the Electoral College to cast ballots are “Electing” the President & VP.
It’s not so clear whether the House, when “choosing ... by ballot”, is “Electing” the President.