Game mode and scores.

You really need to understand this.
You already created your first score when added your game to the escs:
You created here your first score.
Now let think a bit more about this.
Only you know what scores make sense for your game and what scores should be used for the organization of the tournaments. The scores you define here is your way to know others about what it is possible. In the exactly same way as you defined your first score, you can define as many scores as you want. Everybody who wants to organize a tournament will be able to choose from these scores. You just have to submit them in the endGame() method. If you want for some score not to be available to the general public select the non public checkbox.

Game mode

Please take a look now at the Advanced game settings. Specifically at the game mode section.
Take a good look at the game mode section.
As with a game score, you know best which games mode of your game are best suited for the tournaments and competitive play. You can define here as many game modes as you want. Tournament organizers can then choose between individual game modes to set up tournaments. Again the non public checkbox allows you to hide game modes from a general public.
Let's go through the individual fields in the game mode form.
Mode type: this field actually tells whether this game mode in your game is a real multiplayer mode or a single player mode.
Name: give a meaningful name to the game mode.
Description: human readable description of the game mode as you would write in your game.
Max set duration: how long you think one set in this game mode should maximally last. It is an upper limit.
Minimum participants in set: the minimum number of participants that is required to start this game mode.
Maximum participants in set: the maximum or desired number of participants that is allowed for this game mode.
Penalty points: if a player does not attend the game or just leaves the game during the tournament, this player needs to be penalized. His score for this game must be something that definitely makes him loose this game. Enter such a value for this score that makes in sense in this game mode. For example, for Tetris it would be -1 or any negative number.
Set parameters: here you can enter any additional parameters that your game needs to start a game in this game mode. These parameters will be transferred to the game before each match. These parameters must be in a format that your game understands. They can define a particular map or set of items or literally anything you want. Just your game needs understand them.