“Mainstream media”, the expression, means three things to me right now as a member of the general public. You have to have all three attributes to be included.
First, you have to be a somewhat popular source for news and analysis of events. You do not necessarily need to be a for-profit business, or large, or be a legacy producer of television or newspapers or magazines. Medium would be included, according to my definition.
Second, you have to be writing or talking about politics. “Mainstream media” has no connotation related to, say, fashion, sports, music or investing.
Third, in your publishing efforts, you must aspire to share/inform first, to persuade/shape second, and to be transparent with your audience at all times. The essential disqualifier from being “mainstream media” is the use of propaganda — pushing or promoting misinformation, disinformation, lies, half-truths, without the consent or awareness of the audience.
Hannity and Carlson and Ingraham are not “mainstream”, despite their huge viewerships, because their primary objective is to manipulate opinion, but they are not upfront about this. They cherry-pick facts and data, take advantage of people’s emotions and their respect for authority, build arguments using logical fallacies, and do all of it without disclosing to their audience that their main objective is to persuade/shape their opinions and beliefs. They say, “Our goal is to give you information and insight”, but their real goal is to win people over to conservative worldviews and political causes. It’s this deception that disqualifies them from “mainstream” consideration.
Trump has worked very hard to convince people that conservative perspective is the disqualifier, because that allows him to paint the mainstream media as a political opponent. We need to push back on this.