Seems odd that his contract status with the Sharks can be legally disputed but he was also eligible to sign with another team.
Though NHL and its various contracts are a legal intra-NHL construction of their own, all of it still works under the real world laws. So as there are legal principles that apply above the NHL's own litle legal bubble, NHL can't really ignore them.
I can't claim I know anything about the liability and damages law in US, but I know in some legal systems there is a doctrine of "limitation of the damages", where upon damage happening the suffering party isn't allowed to just go fully passive in the situation and be like the tab is now open, but they are required to take such sensible plausible actions that limit the amount of the ensuing final damage.
If now 30 years old Kane would want to argue for the purposes of the damages, that the contractual breach of SJ has caused his expected career earnings (the SJ contract and the subsequent projected contracts) to plummet, Kane really should be able to show that he has bona fide tried his best to recover the projected career earning losses through is own actions.
That means signing a new contract and trying to ensue another contract after that one. The now-terminated SPC says that he's employed as a Skilled Hockey Player, so its only sensible that the League acknowledges that his best marketable skill is being an NHL-level skilled hockey player. It might return to bite the League if they prevented him from doing that.