Is it obligatory to return the greeting of Islam to one who leaves a gathering, and is the one who fails to do so sinful, and does the same ruling apply if the Muslim is on television, whether the broadcast is live or recorded?

Saying Salam when departing is a Sunnah, and responding to it is obligatory, just as it is when meeting, because the Prophet, peace and blessings be upon him, said: "When one of you comes to a gathering, let him greet with Salam. If he wishes to sit, let him sit. Then, if he stands up while the people are still sitting, let him greet with Salam. The first is no more deserving than the last."

If the Salam is conveyed via live television with a general phrasing, such as: "O viewers... Assalamu alaikum wa rahmatullahi wa barakatuh," then responding to it is an obligation of Kifayah (communal obligation). The obligation is lifted if someone else responds. However, if the Salam is not live or is pre-recorded, then responding is not obligatory, because in such a case, the announcer has not actually greeted the viewer; rather, it is merely a vocal narration.