Yes. The Wii Balance Board (RVL-021) is mandatory to play Wii Fit, Wii Fit Plus, and most games supporting it (Wii Sports Resort specific events, Just Dance Wii U/Switch versions use Joy-Cons, but Wii Just Dance uses Remotes).
Without the Board, the game is unplayable. Used boards are inexpensive (~$15-30) but check for battery corrosion.