Instead of getting mad at them, why not join them in the game? It is fun! As long as they don’t have commitment issues and will remain loyal to you, checking out other men/women is completely normal.
Being overly possessive is a sign of your own insecurities and don’t let that ruin your relationship.
7. They might be overly protective/possessive.
It’s a sign of love when your partner is either overly protective or possessive about you. As such, you should not let this be a reason to fight with them, rather try to make them understand that while you appreciate their protective and possessive nature towards you, you (and by extension your relationship) also require your own breathing space to function.