Youtube has the monopoly as the primary social video hosting platform.
It doesn't. It's quite impossible to prevent videos from being hosted elsewhere. And even if you could achieve your dream of forcing Youtube et al to host the content you like, it still wouldn't work if users and/or advertisers leave the platform as you can see now happening with Facebook. So then what - are you gonna force Nike and Starbucks to pay for the content you like?
You can identify a monopoly however you like, but the law has a very specific way of defining one. Lets look at the requisites for determining a monopoly according to the FTC.
"Market Power
Courts do not require a literal monopoly before applying rules for single firm conduct; that term is used as shorthand for a firm with significant and durable market power — that is, the long term ability to raise price or exclude competitors. That is how that term is used here: a "monopolist" is a firm with significant and durable market power. Courts look at the firm's market share, but typically do not find monopoly power if the firm (or a group of firms acting in concert) has less than 50 percent of the sales of a particular product or service within a certain geographic area. Some courts have required much higher percentages. In addition, that leading position must be sustainable over time: if competitive forces or the entry of new firms could discipline the conduct of the leading firm, courts are unlikely to find that the firm has lasting market power.
Exclusionary Conduct
Judging the conduct of an alleged monopolist requires an in-depth analysis of the market and the means used to achieve or maintain the monopoly. Obtaining a monopoly by superior products, innovation, or business acumen is legal; however, the same result achieved by exclusionary or predatory acts may raise antitrust concerns.
Exclusionary or predatory acts may include such things as exclusive supply or purchase agreements; tying; predatory pricing; or refusal to deal. These topics are discussed in separate Fact Sheets for Single Firm Conduct."
https://www.ftc.gov/tips-advice/competition-guidance/guide-antitrust-laws/single-firm-conduct/monopolization-definedExclusionary acts. Check. Control of more than 50% of market share. Check. Youtube is very arguably an illegal monopoly. They also are violating their terms of service contract by restricting use of their platform outside of their agreements as well as acting as publishers while enjoying the liability protections of being a public platform.