paintball vs outdoor game

paintball and outdoor game both are nouns.

Word	Noun	Adjective	Verb	Adverb
paintball	Yes	No	No	No
outdoor game	Yes	No	No	No

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

paintball: a game that simulates military combat; players on one team try to eliminate players on the opposing team by shooting capsules of paint at them
outdoor game: an athletic game that is played outdoors

paintball (noun)	outdoor game (noun)
a game that simulates military combat; players on one team try to eliminate players on the opposing team by shooting capsules of paint at them	an athletic game that is played outdoors
a capsule filled with water-soluble dye used as a projectile in playing the game of paintball