We periodically get the official stats as published by the game developers via APIs.
The stats for each game are then processed according to the rules of the tournament. For example, you might get 20 points for a win, then 5 points for each kill,
These rules are different for various types of tournaments, as well as across different games. This all gets added up. Then your best games by the score are averaged or summed together to produce your final score.