When one person plays chess against many opponents at the same time is called a simul.
Chess master , chess player , participant , patzer(a derogatory term) or player .
You would call a person who praises himself a lot a narcissist.
A "harmonicanist" is what a person who plays the harmonica is called.
a person who tells proudly about himself is a boaster or a braggart.
A person who plays Scrabble is called a Scrabbler. (unofficially)
A drummer or percussionist plays the drums.
accordionist
Guitarist
harpist
a cymbalist
guitarist