Is every game unlawful, and what kind of unlawfulness is it, and what is the meaning of the Prophetic Hadith: "Every play is unlawful except three: a man playing with his wife, his shooting with his bow, and his training of his horse"?

It is stated in the noble Hadith that everything with which a man amuses himself is vain (or futile), except for his shooting with his bow, his training of his horse, and his playing with his family, for these are from the truth. The word "vain" (baṭil) does not mean prohibition, but rather the absence of full reward for it. Everything that aids in truth, whether knowledge or permissible action, is considered part of the truth. The default ruling for amusement and play is permissibility, as long as it does not involve something forbidden or distract from an obligation.