table game vs ping pong

table game and ping pong both are nouns.

Word	Noun	Adjective	Verb	Adverb
table game	Yes	No	No	No
ping pong	Yes	No	No	No

As nouns, ping pong is a hyponym of table game; that is, ping pong is a word with a more specific, narrower meaning than table game:

table game: a game that is played on a table
ping pong: a game (trademark Ping-Pong) resembling tennis but played on a table with paddles and a light hollow ball

table game (noun)	ping pong (noun)
a game that is played on a table	a game (trademark Ping-Pong) resembling tennis but played on a table with paddles and a light hollow ball