Technically Gary is freelance and therefore not bound by impartiality criteria. But the problem is that he is very closely associated with the BBC through MOTD. Consequently by saying what he has, it does make the BBC appear, once again, not impartial.
Why is it so important for the BBC to be strictly impartial? It all comes down to licence payers who represent an entire spectrum of political views from far left to far right, and all points in between. ergo: it's very unreasonable to not be impartial as you are then essentially trashing the views of those who still have to pay for you.
The licence fee goes towards the BBC, and on pain of criminal prosecution, each TV viewer has to pay the licence fee if they are to legally watch any other channel live. Even if they don't watch the BBC. Most people were happy to put up with this while the BBC came across as impartial, but I'm afraid they no longer do.
As far as what Gary said, I personally wouldn't give a crap if he worked for anywhere else than the BBC. He's entitled to his own views and is as free as the rest of us to spout them, however ludicrous his nazi analogy may be. But as a high profile representative of the BBC, he should at least show some respect to those who have to pay his gigantic wage bill, and keep his trap shut until he leaves, apart from football.
Having said all that I do think he handled that situation of a few weeks ago, where somebody set off a phone with sex noises on it during a live match, extremely well, with aplomb and humour. That was really well played.