A way to yes and action and structure into existence.
In nearly any scene, you can create a "game" out of whatever just happened by treating the preceding action as just one way of fitting into a template. You then fit something else into the same template, and presto! the scene now has structure.
For example, if someone says, "President Warshington", you can view the game as "mispronouncing names of presidents" and mention "Roose-a-velt" in your next line. Someone else might then refer to "Eisenpowder".
That in turn might develop into a festival of malapropisms all related to government. At the end of the scene, someone mimes a voting booth and walks in.
Often "games" arise in scenes without anyone consciously creating them. If you are Listening closely, you can mentally articulate what the game is and then play a "next" move.
Note that Continuing The Game is completely different than repeating an earlier line that got a laugh. Continuing The Game is a way to Advance The Scene: it's something new. Repeating an earlier line usually just stops the scene dead in the water. It doesn't open up new avenues, suggest a high bar for the players to jump, or make the audience curious about how the game will continue.
The trick when Continuing The Game is to vary something that came before while holding something else constant. This suggests the template to both your fellow players and the audience. "Aha!" they say, "now I see what's going on. Where will this lead?"
Two players start a scene by droning on about something boring. A third player dives in and says, to the audience, in the tone of a PBS narrator, "When King Lear visited Avalon, all he wanted to do was play tennis," and quickly gets off stage.
The players continue, now in Shakespearean style, making use of tennis. A fourth player enters and says, to the audience, "What was the early Shakespeare's fascination with sports? There are many theories, but no one knows," and gets off stage.
The players continue, now bringing in cricket and basketball. A fifth player enters and says, to the audience, "I know! Shakespeare became a playwright because he wasn't tall enough to play basketball. Everything from Henry IV to As You Like It was an attempt to get revenge on the jocks who teased him in high school."
The players continue, now mentioning revenge and a locker room, but in an Elizabethan accent. The first player re-enters and says, "You are wrong! Even as a sophomore, Shakespeare stood 6'1", quite tall in the 1500s. Shakespeare's true calling was bowling..."
The players continue...
Zany yet magnificently coherent. An original and very tight structure emerged out of nothing. And this sort of thing is surprisingly easy to do. Every new move just pounced on what was already in the scene, varying something and moving things one step forward in that "direction".
How many "games within a game" were in that? Continuing "commentator interrupts". Continuing "Shakespeare" (started with King Lear). Continuing "sports" (started with tennis). Continuing "literary critics argue pet theories" (started with claim that no one knows why Shakespeare was obsessed by sports).
You can take just about any action and view it as the first move of a game--any of an infinite number of games. All you do is arbitrarily seize on some but not all of an action. You view the action a little bit abstractly, and then fill the abstraction with a new concrete. It helps if the action is a response to something that someone else just did.
Suppose that your scene partner swings at a golf ball. You say, "Hoo-eee! That's the best slice I've ever seen." Your scene partner then says, "Ok, now you try."
What game possibilities can we find in this tiny bit of action?
The game could be, "Being genuinely impressed by failed actions."
The game could be, "Sarcastic praise."
The game could be, "Teaching the other guy to do what you just did."
The game could be, "Teaching the other guy to do something badly."
The game could be, "Teaching a sport."
The game could be, "Odd expressions like Hoo-eee."
Any of these could be done over and over, but filling in different specifics each time.
With more action, there are more possibilities for games. Some actions are more "gameable" than others. Part of the skill of Continuing The Game is being alert to especially "gameable" actions.
The game might not be filling in a sentence, but having a kind of motivation. For example, gradually everyone in the scene might reveal something silly that they feel embarrassed about.
A game can be any repeated action and any action can be repeated!
See also: Yes And, Tips And Techniques.