I do not think, it makes a difference who made the decision. PR is about how it looks to the outside.

If you wanted to play it anyways, then your messaging should include something which can be as simple as:

We gave women a choice and they want to play Overcooked, so that's what we're doing.

The thing is, anything you play on that occasion is going to be political, because they could be playing games for fun at any other point in time.

Perhaps taken to the extreme, I would argue that even if all living women came together and decided that it's fun and they want to play Overcooked or similar, they would still want to be conscious of their messaging.

Partially, because non-women will be the recipient of that messaging. Partially, because women's rights have a history that you want to commemorate on that day as well. Would the feminists of the past be happy with that choice, too? Would their sons and grandsons be, that are alive today?

But well, also just because it really isn't hard to do better here. Especially when women were involved in that decision, they would more likely be aware of the struggle and able to steer clear of dumb messaging quite easily.