H I'm with you all the way!
Somewhere I have already mentioned ballet, which could fit in the gymnastics bit.
Angling/fishing has to have its different classes of course: Fly fishing, sea angling, and the more restful fishing lake angling, and whatever else there is to have in this sport.
Conkers, tag, hopscotch and marbles could also be added, to create real inclusive games.
What about wood chopping? For the men there already is beach volleyball, so this would be nice for the girls to watch: muscle men swinging axes. I nominate Highlandscenics for this one.
And the endlessly televised sports like darts, and snooker must be popular, so we may already have gold medal talents here.
More suggestions welcome!