You can use an existing engine. You should do some programming of your own in the context of the game, to solve some problem inherent in the game's design (that's not supported by the engine). And you should be prepared to talk about what you did, show your code, and explain how you solved the problem.

While the above advice is also pertinent, you can raise your chances of getting into the industry by applying to smaller companies.
These types of companies don’t often use game engines such as Unreal Engine 3 etc., and often just make one-or-two-man games over a period of 2 or 3 months, often for iPhone these days.
There are so many of these companies and it is so easy to get into them that your chances of getting into the industry skyrocket if you include these in your target scope, just as a starting point.

But these types of companies are more interested in your ability to make a simple game from the ground up. If you would like to include these companies as a potential starting point, you need to make a simple game from scratch. I would suggest targeting iPhone (but use as little Objective-C as you can; stick to C++) because it is very easy for one person to make what seems like a complete and modern product on that platform, and you can carry the iOS device in with you when you go into the interview.


L. Spiro