Caution: the MF swear phrase occurs in the music. There may be other profanities I didn’t notice. I’m former Army; I don’t always notice.
This video sparked a long string of comments at Youtube and also in the Reddit thread where I found it (he didn’t actually break that guy’s neck, BTW). Not every instance of the Doctor using guns/violence appears here. I can remember several more, and the recent series are not depicted. Maybe it’s hypocrisy. Maybe it’s the nature of a being to fall short of where one wants to be, to have ideals that actions can’t always match. Or maybe, as one commenter said, the Doctor is the Hulk.