Yeeeep, figured that's the one you'd ask about.

[ because it's the term least likely to have an equivalent in a world without Pokémon as partners, or because of her previously noted interest in battling? why not both. ]

Where I come from, battling for fun is a thing that Trainers and Pokémon do. You can challenge people you meet while traveling. Perfectly normal! But that doesn't always mean you will get a serious battle from it. And if a battle is not serious, it is not fun.

So there are also places where people looking for an actual challenge can go. All very official and all. Those are Battle Facilities.