All you have to do is enter the game number into the box on the game menu or after the game is completed. You can pick a random game by clicking the 'random' button to the right of the game number.
To stop people from cheating the high scores you can only submit a score from randomly chosen games, if you entered a game number or you replay the same game again and again, you won't be able to submit your score.
The game numbering system is accomplished by using a seeded random number generator. The game number itself is the basic seed which is used to generate the seeds for all the levels. When each round starts it uses the generated level seed to randomly place the enemies and player. Because the level seeds are built from the game number, they will be the same every time that game number is used. This means that any two players playing the same game number will see exactly the same enemy placement, teleport placement, and so on. This way you can challenge your friends to specific games and see who is the best.