In short: No - the steering wheel works on the Nintendo Switch, but *Need for Speed* is not a Switch game, so it will not run on the Switch version of this title.

Additional details:
- The steering wheel is compatible with Nintendo Switch via USB and will act as a Switch controller if the game in question supports controller input.
- Need for Speed games are generally only available for platforms such as PlayStation, Xbox and PC; there is no official Nintendo Switch version (for the relevant newer titles), so you cannot play Need for Speed on a Switch regardless of which controller is used (and the steering wheel cannot be used on a Switch for this game as a result). (Manufacturer information only shows compatibility with Switch and PC, not PS5).
- If you want to play Need for Speed on PC: the steering wheel works as a PC controller via XInput, so it should work with PC versions that support XInput.

I'm not entirely sure which Need for Speed edition you mean exactly; if you name the specific title, I'd be happy to check if a Switch version exists or if the PC version supports XInput.

It is the game "Need for speed hot pursuit" for the Nintendo Switch 1.