Due to their size and reach, the oil giants have massive political clout. A major reason we do not have carbon taxes yet is because of their ability to lobby (bribe) politicians across the globe. These lawsuits matter because they hinder the companies ability to wield influence. Every dollar they spend on lawsuits and settlements is one less dollar they can spend on lobbyists, climate denial "research", etc...
Additionally, these lawsuits raise the cost of being in the oil business compared to renewables. So the "new actor" is much more likely to be a renewable company, simply due to the fact that investors do not like regulatory uncertainty.
It is worth mentioning that the oil industry is now in support of a carbon tax. On paper, this sounds good. But what really is going on is that they realize that the writing is on the wall and that after decades of opposing a carbon tax, their best chance of survival moving forward is to try to move the conversation away from regulations and towards "free market solutions". But this is cynical for a few reasons, the primary one being that it is much easier to convince a future Republican administration to retroactively lower the carbon tax (under the guise of "job creation" or some other nonsense) than it would be to repeal strict environmental regulations. And the other primary reason is that a carbon tax essentially "kicks the can down the road", i.e. it doesn't actually solve climate change or prevent the fossil fuel industry from continuing to do business as usual. It just makes the price of fossil fuel based products a little higher. Where as a regulatory approach would likely significantly hinder the companies ability to operate and likely significantly reduce the size and scope of the fossil fuel market
This is important, because in the next few years we are likely going to see the oil companies try to get a "seat at the negotiating table" so to speak. So these lawsuits are important because it puts these companies on the defensive, and potentially cuts them off at the knees, hindering their ability to water down future climate change legislation.