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to host links of which they own copyright on their own search engine //
They don't own a copyright on the torrentroom link (for example). There is no copyright in a regular URL¹.
They apparently own the content linked to. But then I own the content of my house that the road network is linked to and that doesn't mean the local government is party to people taking my stuff without asking.
Links may be made unlawful but they're not copyright infringements. IMO they're not even contributory.
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¹ It may be possible to craft a URL that has sufficient distinctiveness and artistic merit to acquire a copyright but I can't ever recall seeing one or hearing of one. A URL could be a trademark infringement of course.