It was a team Canada event so it does fall under their purview. Why do you think the IIHF was able to toss out Team Russia and Team Belarus out of all the international hockey games the IIHF controls? When you join the IIHF, all countries agree to certain standard and one clause consists of teams do as part of team functions. IF it was the Edmonton Oil kings or Vancouver Giant, team functions, they the IIHL would have zero power.
Both the FInnish and Swedish federation are watching what is going on closely and believe that Canada is dragging its feet hoping other people will forget about it. My guess is that we will see some Canadian players named, banned from the international stage and some sort of admonishment from the IIHF in how Canada handled the situation