table tennis vs table game

table tennis and table game both are nouns.

Word	Noun	Adjective	Verb	Adverb
table tennis	Yes	No	No	No
table game	Yes	No	No	No

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

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

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