Even if you find a game that has a gender balanced community, that's no guarantee that it will be as attractive to an equal number of each gender on your team. Also if you're going for gender equality why would you not also go for racial and ethnic equality too? At my last job we had three developers from Nigeria. All thought games (excluding actual physical sports) were for children and looked negatively upon adults who played games. How would you not end up excluding them?

Having been the person that despised going to the various sportsball games that everyone at the company went to, and wound up being excluded without so much as a second thought? I'm not sure I'd worry too much about excluding them. No matter what you pick, there's bound to be some people that just can't enjoy it.

Why pick only one thing? If this is a weekly or monthly event, there’s no reason it has to be the same every time; why not have a variety of events on rotation so that you’re not alienating the same set of people every time?

So why not Fortnite?

are you using the statistic to imply that women would be less likely to enjoy fortnite in the first place, or that they would be more likely to encounter embarrassment what would be a work-related event?

if the game isn't as appealing to women for whatever cultural reasons, it's probably not appropriate to endorse it for team building. if the pervasive harassment is the main concern, this is much easier to work around. very little is lost by disabling area comms in battle royale games; I usually disable it because I don't want to hear fifty people eating their mics in spawn. in games like CS, you can just host a private server for a trivial amount of money.

in general though, I have mixed feelings about company events after work hours. inevitably, there will be people who don't care for the "fun" activity and but feel obligated to participate or worry about missing networking opportunities if they don't. especially when it comes to something like videogames, it's quite easy for people to organize this stuff themselves without an official endorsement from the company. I don't really see any reason why a company should go beyond just giving employees space in slack to organize activities outside of work.

How does the fact that Fortnite is more popular among males equate to females being less likely to be able to be good at it?

Or people who just don't like these types of games (inevitably variations of first person shooters), of any gender...

What is a game that you would consider gender-balanced, if that's even a thing?

Something like Mario Cart maybe? The concept of an easy to learn, yet still competitive racing game exist on most platforms.

League of legends I've noticed is pretty popular among women too.

I like that idea. Nintendo is pretty great at creating games that appeal to pretty much everyone.