Perhaps you can show your potential by actually CREATING some video games and then show them to the admissions officer.
There are plenty of resources available for creating video games...
You can go to the following websites which has whole bunch of FREE programs, tutorials, and other information for game programming:
http://www.instantfundas.com/2007/10/game-maker-create-your-own-games.html
http://www.ambrosine.com/resource.html
Books for Game Maker program (Not free):
http://www.amazon.com/Getting-Started-Game-Maker-Jerry/dp/1598638823/ref=sr_1_2?ie=UTF8&s=books&qid=1250760444&sr=1-2
http://www.amazon.com/Game-Makers-Apprentice-Development-Technology/dp/1590596153/ref=cm_cr_pr_product_top
You can also get Video Game Tycoon for about $29. Yes this is NOT free but if you read the customer reviews for this product it is a good program that let beginners create their own video games:
http://www.amazon.com/Video-Game-Tycoon-Create-Games-Pc/dp/B000KJW71Q/ref=sr_1_1?ie=UTF8&s=videogames&qid=1250426348&sr=1-1
You can also go to an online book store like www.amazon.com which would probably have a whole bunch of good books and programs for game programming:
http://www.amazon.com/Beginning-Flash-Game-Programming-Dummies/dp/0764589628#
http://www.amazon.com/Game-Programming-Teens-Maneesh-Sethi/dp/1598635182/ref=sr_1_17?ie=UTF8&s=books&qid=1250425837&sr=1-17
http://www.amazon.com/Game-Programming-Teens-Maneesh-Sethi/dp/1598638432/ref=sr_1_2?ie=UTF8&s=books&qid=1250443014&sr=1-2
http://www.amazon.com/Enteractive-DarkBASIC-3D-Games-Creator/dp/B00005V57T/ref=sr_1_2?ie=UTF8&s=software&qid=1250845081&sr=1-2
http://www.amazon.com/ENTERACTIVE-FPS-Creator-Windows/dp/B000BTAC30/ref=sr_1_6?ie=UTF8&s=software&qid=1250845311&sr=1-6
Sometimes it would be better to get a good book for game programming because it would probably show step by step on how to produce a good video game and it usually would include a CD which includes programs, code, instructions, and etc. which would help you to learn game programming and create your own video games.
P.S.
If you want advice on becoming a game programmer then you should contact the above book authors who actually have WRITTEN books about game programming!