A person who plays the drums is typically called a "drummer." Drummers are essential members of musical groups, providing rhythm and tempo. In the context of Marching Bands or orchestras, they may also be referred to as percussionists, which encompasses a broader range of instruments in the percussion family.
A "harmonicanist" is what a person who plays the harmonica is called.
A person who plays Scrabble is called a Scrabbler. (unofficially)
A drummer or percussionist plays the drums.
accordionist
harpist
a baritonist
A saxophonist.
guitarist
Guitarist
a cymbalist
A pianist.
The umpire is the person that rules on plays.