YouTube doesn't control anything about the endpoint which it is streaming video to, it just has control over how their servers respond to different requests
not as antitrust laws are written, no. not a sherman section ii monopolization of trade or commerce, not a section i restraint of trade, not a clayton tying. as with most antitrust cases, it comes down to market definition. the reasonable market is phone messaging or some such; the only way to win would be basically defining the market as imessage itself which no court would suffer since whatsapp and similar are free with equal or greater features.
you can argue antitrust statute should be expanded or changed, but there's no reasonable case as things stand.
It's not just the way they are written, it's also the way they are interpreted. Antitrust used to have a lot more teeth pre-Bork, among other things, because it was much more proactive in terms of anticipating negative effects on the market even before the company would become a glaringly obvious monopoly.
you don't necessarily need a monopoly to have a "dominant marketing position". being one of the two major OS's and losing access to 30-50% of a nigh-universal market because the its not in the interest of the platform's profits would definitely count as an anti-competitor move utilizing the company's weight. AKA anti-trust.
Also, the relevant market doesn't have to be "Americans." It's completely reasonable for it to be "teens in San Francisco" or the like, if that's the group of people you need a messaging app in order to interact with.