It's not even copyright, they're suing for using things they patented, but their patents are extremely general. I kid you not, they have a patent for MOUNTING CREATURES, something hundreds of games have done.

Abstract: In an example of a game program, a ground boarding target object or an air boarding target objects is selected by a selection operation, and a player character is caused to board the selected boarding target object. If the player character aboard the air boarding target object moves toward the ground player character automatically changed to the state where the player character is aboard the ground boarding target object, and brought into the state where the player character can move on the ground.

I'm no lawyer so I can't tell you how well this would hold up in court but it's ridiculous. See more: https://patents.justia.com/assignee/the-pokemon-company