The best definition I've seen that is all-encompassing, but kind of general, is the following: the game of the scene is the thing in the scene that is funny. I suppose the next question is: How do I know what is funny?
So the textbook UCB method is to first start by looking for the "unusual thing." Usually the unusual or weird behavior in a scene will lead to a funny concept. Let's say there's a scene about waiting in line at the movie theater. You could just do a scene that mimics reality 100% where you stand there making small talk and slowly moving down the line. That's a pretty boring scene with nothing happening, although that is 100% realistic.
Instead, lets say you're waiting line line but then discover that your friend ordered a bunch of popcorn, candy, and soda. Boom. There's the unusual thing. Now we have to apply the "if that's true, what else is true" formula, in which case we discover that the friend likes to act as if the theater is his home. Meaning he could start putting on pajamas, ask his mom to drop off some food at the theater, etc. The game has now become "guy who acts as if the theater is his home".
A great exercise to practice this technique is by doing scenes with the key phrase "I think it's weird that you..." When someone in the scene says that line, the improvisor is really saying "Hey, I found something weird, I think there might be a game here" To which the other player should try to get on the same page and hone in on the game.
For example, in the movie scene above, the first player could say something like "I think it's weird that you bought so much food." The second player could then say "Oh yea, I like to eat a lot, just like when I'm at home..." Then the game can be played from there.
Give it a shot!