Next week is the OpenSauce exhibition and my booth will have a TI-84 Plus CE gaming competition where attendees can win a modified TI-84 Plus CE! I need some help picking out the ideal game however.

I have some criteria:

• The game must have some scoring system built in so I can objectively award a first place.
  
• The game shouldn't take the average person longer than 5 minutes to win or lose. There will be potentially hundreds of people and no one should have to wait around to play. I will have 2 calculators going simultaneously so any wait shouldn't be too bad.
  
• The game should preferably demonstrate the capabilities of the CE and the programming behind it. (Basically a Wow factor)
  
• The game should preferably be somewhat familiar to the average person.

Some of my top candidates:

Calcuzap: Stores top 12 scores with names. Lots of very smooth graphics. Adjustable difficulty so I can balance fun with how long each person plays. Similar to Galaga which is somewhat familiar to people.
PacMan: Stores top 5 scores with names. Doesn't take too long for the average person to die. Extremely familiar to people.
Tetris: Difficulty ramps up pretty quickly. Extremely familiar to people.
Dino Run: Difficulty ramps up quickly. Smooth graphics. Extremely familiar to people.

Let me know if there's any other games I should consider!

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Competition rules:

• Each attendee has unlimited attempts but must pass the calculator to the next person after their attempt is over.
  
• When the attendee's attempt is over, they will enter their score, contact info, and preferred calculator in a google forms. (All data will be deleted promptly after winners have collected their prizes.)
  
• The person with the highest score at the end of day 1 will be selected. A tie will be broken by whomever got the score first. No awards will be given until the end of day 2.
  
• The person with the highest score at the end of day 2 will be selected. The winner from day 1 cannot win day 2 but can still play for fun. A tie will be broken by whomever got the score first.
  
• Of the 2 possible winners, the winner with the highest total score will receive their calculator of choice. A tie will be broken by whomever got the score first.
  
• The winners will be contacted at the end of day 2 and they have 3 days to provide a way of collecting their prize. After 3 days the 2nd place winner for that day will be contacted.

Bit of self-promotion--maybe HailStorm would be a good choice. It has smooth and nice-looking graphics, powerups, bossfights, and a bit of strategy.

Calcuzap is somewhat similar to this, though, and the fact that it can store those 12 high scores could be the differentiator.

CMonster would also work well, I put a lot of time into that back in the day. Or perhaps it could be a GameBoy game played using TI-Boy CE?

Honestly anything on this list is a good fit for your requirements and a worthy option.

Donkey Kong CE is another familiar game with a scoring system and leaderboard which I think could also be a good choice.
CEleste has a scoring system (speedrun timer) and interesting gameplay, smooth graphics, etc, though it's a bit of a longer game in terms of most average runs and is lacking a scoreboard. Probably not a good choice for what you're trying to do but I still think it's worth a mention.

Hopefully you'll be able to feature some other interesting programs besides those involved in the competition though, since there's a lot of other interesting projects as well

Edit:
Forgot about FlappyBird, but this could also be a good one.
KingDubDub's Jetpack Joyride is an impressive recreation though I'm unsure as to how complete the current version is.

Thanks for all your suggestions! I ended up going with Calcuzap and it was a great choice though it could be improved with some tweaks.
Storing the top 12 scores was really nice since not everyone wanted to win the calculator, they just wanted to play.

The only downside was that the game quits automatically after a minute on the home screen and doesn't remember the last difficulty that was set. This meant I needed a friend to set the game up almost every time a new person wanted to play. I get why the game acts like this (most people wouldn't want the game to drain their battery) but next time I'll make some tweaks to the included source code to disable timeout and lock a difficulty.

I made a shell program in TI-Basic for my assembly games (long story), and the fact that Calcuzap ends after a single round drove me crazy, so I set it to restart the program if you're pressing [enter] at the time it ends. It also archives the AppVar that saves the names and scores when you quit. I didn't know that it quit after one minute on the home screen, but you can get around that using Celtic CE.

:Lbl 0
:"CALCUZAP
:det(70
:startTmr→T
:Repeat checkTmr(T:End
:If getKey!=45:Goto 0
:"rowSwap(CZapHigh→Str0
:det(5

Of course, you probably already knew that.