Sorry, but you're not even close. Apart from anything else, the game you're referring to where a ball is thrown back and forth is just called "Catch", not "the catch". As has previously been said, "What's the catch?" is a standard idiomatic phrase used in English.
As explained earlier, "what's the catch?" is asking where the hidden disadvantage is in something that seems to have only advantages. Refers to the situation.
"What's your game?" is asked to the person who you suspect may be trying to trick you. Similar to "What are you up to?". Refers to the person.