So if they win, the US taxpayer will pay for it?
The money that has passed various deadlines may be more difficult to return, however it is still money that is due to Nintendo. That may be more difficult to obtain, but it isn't the government's money in the first place.
US tax payers aren't paying money to Nintendo - they're paying for the government's lawyers to try to argue against not paying back illegally collected tariffs.
https://realeconomy.rsmus.com/ieepa-tariffs-struck-down-what...