I can understand your confusion about the difference between what a games is and what a sport is.
There are many different definitions of both in dictionaries and on English websites.
In general both sports and games can have
winners and losers and both are usually
competitive.
The word sport or sports
includes games.
e.g Soccer is my favourite
sport and tonight I am going to watch the
Barcelona game.
Here
game is specific describing a specific competition in which Barcelona is playing.
Swimming or running are
activities and both can be used in a sport or game.
e.g you run to play the game of soccer.
e.g you swim to pin a game of water polo.
You could say that both running and swimming are
activities which are used in sports and games.
Here is a link to a site that might help you understand all of this much better. I hope it helps.
https://learnersdictionary.com/qa/What- ... and-Sports