There are several point worth unpacking here. First, let's take Gregory's defense of the question in which he argues that the question was legitimate because other people had raised it. In effect, Gregory is just JAQing off, and this is clearly an example of a Loaded Question. This is, of course, when one asks questions that contain significant assumptions buried within them such that one can't answer the question without acknowledging the assumption buried in the question. In this case, Greenwald can't answer Gregory's question without admitting that he committed a crime by aiding Snowden. Greenwald responds to this question in the only effective way by actually looking at and making explicit the assumptions buried in the question. It is this unpacking of assumptions that reveals many of the filters that are at work on Gregory.
To begin, we can see a really nice example of Flak. This is criticism aimed at the media by powerful elites in an attempt to discipline the media. In this case, Gregory is attempting to minimize the character of Greenwald in the hopes that this will minimize the impact of the story. By calling into questions Greenwald's status as a journalist (and he is more clearly a journalist than Gregory), Gregory is attempting to minimize the significance of the story. He accuses Greenwald of being an "activist" with the implied assertion that we don't have to listen to Greenwald because he has some political axe to grind. We can clearly see how Gregory's demeanor towards and questioning of Greenwald are designed to minimize the significance and importance of the revelations he has been reporting.
A second filter that Gregory is operating under is what I have been calling Jingoism. This is a reflexive and unthinking patriotism that presents everything our government does as good, and anything opposing our government as bad and evil. We can see this is Gregory's knee-jerk criticism of Greenwald as someone who is unAmerican and "bad" for leaking these secrets and revealing the criminal misconduct of the government. Gregory would apparently prefer that all this information remain secret so that he doesn't have to bothered by it.
Lastly, we can see the media's desire to only listen to and talk with "approved" sources. Gregory was essentially forced to have Greenwald on his show because the story is so big, but one can see Gregory's discomfort at having to interview Greenwald as well as his attempts to marginalize Greenwald by suggesting that he isn't a "real" journalist and thus need not be taken seriously.
It is important to stress that I am not trying to argue that Gregory is receiving special instructions from his government paymasters. It doesn't work like that. Rather, Gregory is just echoing the mindset of his employers at NBC, and the general mindset of the Washington Press elite. Gregory is close friends with the people who are implicated by this story. Furthermore, the story makes him look like a lousy journalist since someone outside the Mainstream Press has managed to break the most important story of the decade, so naturally he is a little prickly about it. The story implicates people he is close to and it makes him look bad, and this, I think, sufficiently explains his treatment of Greenwald in the interview.
h/t to Digby