A:Answer The headset would work in any game that you have chat capabilities in.
The Game or Switch console itself is what may prevent you from chatting with other players on other consoles, so you would want to check your Game's chat settings and ensure that you have all the necessary settings required by Nintendo in order to chat on their console.
As a heads up; some of Nintendo's games require an additional subscription service for chat purposes, and then those chat capabilities would only be accessible via a separate smartphone app.