I share your concern about the flawed argument that there is a pay gap issue between male and female athletes. A discriminatory pay gap exists where persons are performing the same job, but are being paid different amounts. For starters, I note that if a team owner could pay a player of equal ability a fraction of the salary he or she paid a second player, the team owner would have a tremendous incentive to hire the lower-salaried person to replace the second player (this is true for any team owner with limited resources interested in putting together a good team). Doing so would free up money to sign more expensive players and improve the team's overall performance. Older athletes (male and female) face this issue all the time as they are replaced on teams by younger, less expensive players.
Women athletes are in different leagues because they are not performing the same jobs. They are playing in inferior leagues that have smaller venues, less spectators, fewer sponsors, and lesser lucrative TV deals. The owners in those leagues have less money to distribute as salaries to players. Whether there is a salary cap or not, the salaries paid to players are largely market-driven decisions that have nothing to do with gender.
Salaries paid to athletes are generally not political decisions (I concede that perhaps in a country like North Korea, salaries may be decided by a central authority and perhaps the athletes make the same amount of money for their services – I do no plan to relocate there to sample their version of equality). In most Western economies, payment for services is largely an economic, not a political decision. If one were to argue that male and female athletes should be paid the same, the proponent would have to confront the issue of who is deciding the pay rate for athletes? In a market, the rate is set be both the voluntary agreement of thousands of employers and thousands of employees. Equal pay can be accomplished by lowering the pay of male athletes or raising the pay of female athletes. Are the male athletes overpaid or the female athletes underpaid?
When someone suggest that an employee is entitled to equal pay, they are arguing that the government should be deciding what the employee earns. I respectfully suggest our government bureaucracy is not competent to determine the relative salaries of Lebron James and Diana Taurasi (perhaps the best players in their respective leagues).