I have no insight into this project.
But I have been on the side of the license holder, and on the side of doing personal projects that violated licensed IPs and getting (very polite) requests to desist what I was doing so the license holder didn't have to report me to the source. To which I complied, they were in the right, and I wasn't.
As the license holder you are paying money for that license. Perhaps up front cash, perhaps a royalty on everything you sell, and putting your own time and money into developing something with it.
Unauthorized, unlicensed projects hurt that investment.
If say exA (pure speculation from here on out) was working on an arcade release of the Campaign mode, with Cave's approval, they're not only paying Cave for that, they're also paying their devs, or Trap and Mike, or whoever to make a port.
They hope to attract shmup fans to the arcade to play it, and make money for ops who buy their game. They hope to sell their game to private collectors. Their business model relies on having exclusive content their fans are excited about.
If that core, and frankly small, audience can simply play it for free? It's going to hurt sales, it's going to hurt arcade plays.
So yeah, they have "the right". Legally speaking they would probably simply ask Cave to deal with it, but before anyone sends a cease and desist and involves lawyers a simple polite email often gets the job done. Nobody here is trying to invite problems for the companies or the community.
Or maybe something different happened, who knows. But the above isn't unreasonable. Sharing a fan remake of a rare piece of IP is neat, I'm 100% for it. But it's not our IP, and the holders do have rights.