From their website:
Metro Vancouver Kink is an incorporated, non-profit society.
That is, they are a corporation and corporations are legal people, capable of suing and being sued just like natural people are.
The lawsuit alleges defamation which a corporate entity can do by making untrue statements that damage someone’s reputation. Based on the linked article, I can’t see that this is “retaliation”; the statements made are, if untrue, almost certainly defamatory and the defamed person is legally entitled to be “made whole” as far as possible.
Incorporation is a method of shielding the members of the corporation from the corporations liabilities, legal or otherwise. From the article, it appears the allegedly defamed person is also suing the directors of the corporation - directors are usually legally shielded unless they have breached their duties as directors.
One final point, not-for-profit entities still make profits or losses (called surpluses and deficits) and holds assets and liabilities just like a for profit business. Indeed an entity must at least break even over the long term if it wants to survive and make surpluses if it wants to grow. The difference is that a non-profit cannot return those surpluses to its members the way a company can; it has to use them for the purposes for which it was established or for defending lawsuits or paying out damages.