He misses ____ with his friends.

admit, consider, delay, dislike, enjoy, escape, excuse, finish, forgive, imagine, insist, keep, mind, miss, practice, prevent, risk, suggest, understand ইত্যাদি verb-এর পরে verb-এর gerund form বসে।
তাই play এর gerund form হিসাবে playing বসেছে।

Source: British Council Website.