These players aren't forced to play or are they at risk from the game itself. How is someone allowed to file a lawsuit? If that was the case every employer that has people at work would be in the same position.
Employers are in a different boat because of workers' compensation insurance and the statutory protections they are afforded by most states so long as they maintain coverage for employees. But even there, it is state specific, and "occupational diseases" are more likely to be covered versus "ordinary diseases" encountered in normal life. For example, I can't file a worker's comp claim against my employer if I get the flu from a colleague in the office. But if you work in certain industries (like healthcare, as a first responder, or in corrections), covid-19 likely qualifies as an occupational disease (meaning people in these fields infected by covid-19 on the job can probably file a workers' comp claim, but they probably can't file a lawsuit). Basically, if an employer has workers' compensation coverage for covid-19, it's very difficult to file a meritorious lawsuit.
But assuming a circumstance where there is no workers' compensation.... Where an employer has covid-19 policies and procedures in place to promote a relatively "safe" environment, the employer asks its employees to come into the office, the employer does not follow its own covid-19 policies and procedures, the failure to follow its policies and procedures results in several employees contracting the virus and being hospitalized (or worse) or otherwise injured, and through contact tracing or otherwise employees are able to demonstrate the infection more likely than not occurred at their place of employment, there is a good chance a lawsuit can be filed (depending on the jurisdiction). As I type this, Celebrity Cruises is dealing with a class action lawsuit filed in federal court in South Florida for exposure to covid-19 (that's admittedly a bit different than the usual circumstance because maritime law applies).
Some states have passed laws to expressly protect employers/businesses from covid-19-related lawsuits. Some states have expanded workers' compensation to include covid-19, further insulating employers from claims (absent gross negligence or willful conduct). At this time, I don't believe Florida has, though the situation is fluid and I know it has been raised by the state legislature.
But either way, players aren't employees. They don't get paid. On that basis alone there will be a difference in how the law treats sick athletes exposed during a game vs. sick employees exposed at work.
Still an uphill battle for various reasons, but nowhere near as tricky as in an employer/employee context.