I hate the term "capitalist," Marxist rhetoric has pervaded the academy, much of it used by people who have never read Marx (I had to read all three volumes of Das Kapital in graduate school), have no acquaintance with the history of economic thought, and don't realize that Marx is outdated as Freud, important in the history of thought, but basically irrelevant in today's world (Marx never read or ignored Marshall, he was basically a sociologist, not an economist).
Yes, there is capital, there is labor, there is technology, there are power relations and market structure. There are markets, but "capitalist" implies a mode of analysis which is wrong headed and outdated. It depends on the labor theory of value, which simply is bad economics.
Players couldn't make a dime without stadiums, TV, etc. and the human capital developed by the minor league system.
So it's not like they've "earned" this money which is then expropriated by owners, it's an entertainment industry, in which all parties make an investment (financial, human capital) and earnings depend on both value created (i.e. entertainment value which is what produces revenue) and bargaining leverage. A team can be owned by a single rich man, or in the case of the Green Bay Packers, a collective. Players could own teams (and some are part of ownership groups), but there's a good reason most aren't interested, few have enough money for a majority interest, and a minority interest isn't the best investment in the world. And the transactions and opportunity costs (not to mention ego issues) of players banding together to buy out the owners precludes that happening in the real world.