I don’t think it is a monopoly
It is just one leg of the entertainment industry in this country
I get your point, but it’s really a matter of degree. If you take that argument to its extreme you could make the same argument, that power companies are not a monopoly because consumers of power can always choose to do without and spend their money on something else.
The market for football is sufficiently unique that it has a low substitution effect ,i.e. consumer behavior is slow to respond to increases in price by spending their dollars somewhere else, which indicates it has a high degree of uniqueness, and that other products make a poor substitution for it.