I mean, Nintendo probably does benefit, but I can't see how there's a case here.

The government does have an obligation not to impose illegal tariffs on importers.

Nintendo doesn't have a legal obligation not to raise prices. They, as with pretty much any vendor, can charge whatever they want. You can't win a court case unless they did something illegal.

What limits them from doing that is that they'll lose sales, especially if competitors don't.

Companies could have gambled on the tariffs being overturned in court (as they were) and eating the losses with the hopes of recovering them later. That's a risk, but some companies did do that. They benefited from gaining sales from their competitors. Nintendo didn't take that route; they probably lost sales, but they also avoided the issue of taking losses on a per-sale basis.

EDIT: Well...okay, if you could show that Nintendo tried to get the tariffs imposed and then overturned as some sort of intentional mechanism to cause many vendors to increase prices without incurring actual costs to themselves

which I am confident that they didn't do, but using it as a hypothetical

you could maybe make some kind of antitrust case on price-fixing. But it doesn't sound like that's what the lawsuit is claiming, and in any event, what would be illegal there wouldn't be collecting the refunds.