Basically, you can still work on your game after the deadline. You could even submit an unfinished game.
The point being that when the judges are playing your game, and if something is broken or incomplete, it would probably count against you and reduce your chances of winning. So to be safe, you should have everything completed by the end of the contest date.
You don't need to submit any code, nobody needs to see it. You made the game, and the game belongs to you and nobody else

After the contest is over, it's still your game and hopefully it will become a popular game!