There are many benefits of question games because they spark creativity and help people focus attention on the outcome of the questions. Examples are to ‘learn things’ like Trivial Pursuit teaches, or ‘combine random themes’ (Cards Against Humanity), or push the mind to ‘think faster’ (Charades), or ‘consider thought-provoking questions’ that might not normally be asked (How Game Are You?™ Couples Edition). Whatever the purpose of the game is, questions and answers create the outcome and so the better the question often the better the outcome.
Questions are also a great personal skill which everyone should develop, so question games motivate you to play more of these, give ideas and first-hand skills on asking good questions, demonstrate different question types and even give examples. Whatever position or occupation you may find yourself in, there are appropriate questions you should also ask to get the clearest pictures of things, or about people, and these can be used in conversation, building rapport, developing a relationship or gamified just for fun and connection. Games are fun ways to learn these skills and have fun with your friends at the same time.
To get you started, here there are some game examples that all use questions in different ways: