I've seen only three "game show" letter segments so far (for the letters P, W, and Y). Other than the letter and the specific items Cookie fetches to win, the game is fairly predictable:
1. Cookie Monster hears a voice-over announce the game show, the rules and the prize ("lots of cookies").
2. After the clock appears onscreen, Cookie asks what the letter of the day is; the announcer names the letter, which appears in another corner of the screen.
3. Cookie's "three things that begin with the letter ___" follow the same general pattern: one food item, one non-food item (which Cookie still eats if I remember correctly, and then Prairie Dawn (who usually protests being dragged onscreen).
4. The announcer says that Cookie has made a mistake and forfeits the prize, because "girl" and/or Prairie's name begins with the wrong letter. (Of course, her name isn't a problem in the P version of the game...)
5. Cookie Monster argues that his third find should count, either because of Prairie's name (in the P clip) or the condition he found her in (wet from a shower in the W clip, yawning after he wakes her up in the Y clip). The announcer gives in, and a shower of very fake-looking cookies begins falling onto the set.