YOU SAID:

They are playing a cool game

INTO JAPANESE

彼らはクールなゲームをプレイしています

BACK INTO ENGLISH

They are playing cool games

INTO JAPANESE

彼らはクールなゲームをしている

BACK INTO ENGLISH

They have a cool game

INTO JAPANESE

彼らはクールなゲームを持っています

BACK INTO ENGLISH

They have a cool game