How to make a competition input form and a view?
To avoid writing a manual (to answer your question), here is a blueprint ...

Content type Game

Create a content type "game", with 2 entity ref fields to another content type like "player", and the other fields like date, etc.

3 Rules Components

Create 3 similar rules components (with parameters the score for player 1, and another parameter for score of player 2):


a 1st Rules Component with a Rules Condition to check if player1 has won, in which case you perform a 1st Rules Action to "set a data value" to set the "comp score" for player 1, and a similar 2nd Rules to set the "comp scrore" for player 2. Then add an extra Rules Action to save the entity (to ensure the comp value is also saved).
a (similar) 2nd Rules Component to check if player2 has won.
a 3rd , and one if the score was equal.


Custom rule

Create a custom rule like so:


Rules Event: before saving content of type "game"
Rules Actions: Perform 3 Actions, whereas each of these action performs one of the Rules Components create as described above.


Create a view games

Create a view of all your games. In doing so, use the Views Calc module to "add up the scores".

PS: I'm assuming this question is about D7.