"The Battle of the Sexes" Main Character? Protagonist?

Judging from the trailer, I anticipated “The Battle of the Sexes” to be a comedic gender fight between Bobby Riggs (IC?) and Billie Jean King (MC?). As the story progressed, however, Bobby seemed very much in pursuit of having the battle, a good candidate for protagonist. Acts 1 and 2 focused so much on their respective personal concerns, with amazingly little time devoted to the tennis match. Actually, in what’s probably the beginning of the 3rd Act, Marilyn — Billie Jean’s secret lover — tracks down Billie. Billie smiles upon seeing her and introduces Marilyn as her hairdresser. In this Act, Billie refuses to participate in the match, which makes me wonder if she’s the antagonist. Yet, she’s voicing what’s likely the intended argument of the movie’s writer: that women deserve opportunities only given to men. So what is the goal? I wondered if Marilyn is the impact character, and that Bobby’s personal concern with his wife occupies a parallel throughline. In any event, what seems like a muddled story Dramatica-wise inspired in me a desire to watch footage of the actual match.

Now, having seen the finale, I caught the Alan Cumming character’s private moment with Billie. He says that sometime people will be free to be and love whom they want. In the epilogue titles, it says Billie Jean then continued her pursuit of rights for women and lesbians. So, is the story’s judgment bad because we can see her crying in the gym before the Alan character’s pep talk? Is it good because she’s smiling after the pep talk and because she will eventually be awarded the presidential medal for her feminist efforts?