How is a video service like Daily Motion not a direct competitor to YouTube? As I said, not every social network or service covers exactly the same market but there is a lot of crossover. For example, Facebook can be a good substitute for some Youtube users without being a good substitute for every single one. And it's certainly true than many youtube users have facebook accounts and vice versa.

The web site you cited statistics from seems to imply that their numbers are based on visits: "YouTube's market share of U.S. video and multimedia site visits was 78.8 percent." contrary to your opinion that length of time spent on site is what matters. As such, those numbers contradict other easily found statistics (from Alexa and Wikipedia among others). At least in terms of unique visits. Conveniently, you have to pay the web site that you cited if you want to know where their numbers come from. What legally constitutes market share? Number of registered users, unique visits, total visits or the total number of minutes spent? From an advertising perspective (and that's how these sites make their money), unique views matter the most in my experience which is one reason why it is a separate statistic.

Also, I'm not using some hard to find "alternative" definition of monopoly. I'm using the dictionary definition. The first one. However, reading through the legal definition you posted, a company generally must have between 75 and 80% market share AND there must be "significant barriers to entry". I posted statistics from reasonable sources show that their share is below 75% (even discounting facebook and relying on more direct competitors) and even what you posted has them barely above the 75% minimum. But again, it depends on the legal definition of "market share" in this case. Legally speaking, who gets to decide what is part of youtube's market? The website you cited includes Netflix and Hulu. Well, if you are going to include those then why wouldn't you include network television and cable channels as well? And what about Amazon Prime? Or physical video sales and rentals for that matter? And what are the "significant barriers" to entry that youtube is putting up? There are none as far as I can tell as there are new startups all the time (the aforementioned Bitchute and DTube come to mind, then there is the new CBS pay service if you want to include that sort of thing).

Then there is the fact that they don't actually sell a product (other than advertising). Legally speaking, I'm not sure how that would play into a monopoly claim.

I certainly don't believe government should be providing any kind of protection or special benefits to Youtube but I also don't think they should be punished by them for being successful either. If all the people bitching about youtube would just go to another service then youtube's market share would decrease anyway.