Yes. Ball is a word and so is game so that makes it a compound word.
The noun 'ballgame' is a singular, common, abstract, compound noun.example: I have some friends coming over to watch the ballgame at four.
ballgame ballpark ballroom
ballgame endgame
ballroom ballgown ballpark ballgame ballpoint
A ballgame is a game played with a ball.
Pelota
Jack Norworth
The Mesoamerican Ballgame.
Mesoamerican ballgame
Jimmy Ballgame
Yes
Take me out to the ballgame