The more common way of putting it is "roll for initiative," but I don't know how game-specific that phrasing is, and I'm aware not everyone reading this knows common RPG mechanics.
(That latter part is also why I left out any mention of initiative modifiers that they'd to their dice rolls.)
Like George, I've mostly experienced Table Top RPGs by listening to others play them, and I have noticed that combat turn order just sort of happens instead of being rolled for.
Part of that could be the context of the games being played, that being with an audience in mind, but it also just seems to happen naturally at times when things are happening quickly, and an organic order of actions presents itself.
In the case of the last fight in this game, Nanase ran into a room, ran back out, was chased, and the first person they naturally ran into (Rich) responded. The third enemy who would've been right behind the other two got to do something, Ellen selected George to act next, and that was that.
That, to me at least, felt like a situation where you might skip rolling to see who acts in what order, and just go with what seems most natural.