Let's imagine we are playing a game of spinning a coin and betting £1 on which way up it lands. I bet it will land "heads" up. It lands "tails" up, and so I pay you £1. You have gained £1, and I have lost £1. That is a zero-sum game.
Now, suppose that every time we played the game, the loser had to put an extra 10p into a collecting pot for charity. This time I guess correctly, so you pay me £1, and put 10p into the collecting pot. I have gained £1, and you have lost £1.10. That is not a zero-sum game.
In real life, let's suppose you sue me for libel and win. The court awards you £1000 damages, which I have to pay you. So I lose £1000, and you gain £1000 - which would be a zero-sum game.
However, if one or both of us has hired lawyers, their fees will have to be paid, and that will make suing me not a zero-sum game.