paintball gun vs game equipment

paintball gun and game equipment both are nouns.

Word	Noun	Adjective	Verb	Adverb
paintball gun	Yes	No	No	No
game equipment	Yes	No	No	No

As nouns, game equipment is a hypernym of paintball gun; that is, game equipment is a word with a broader meaning than paintball gun:

paintball gun: an air gun used in the game of paintball; designed to simulate a semiautomatic
game equipment: equipment or apparatus used in playing a game

Other hypernyms of paintball gun include air gun, air rifle, airgun.

paintball gun (noun)	game equipment (noun)
an air gun used in the game of paintball; designed to simulate a semiautomatic	equipment or apparatus used in playing a game