Yes. They sold the exclusive right for lot's of money. In some countries even with a Multi-Laser approach where one station is allowed to transmit live and another station is the first one being allowed to use snippets for summaries.
> Should I have to track down specific moments in a game using my own recording in order to be able to discuss it?
No. You are not supposed to track it. You are supposed to see the programs so they get high ratings and refinance their license.
That's how the deal works and it's a constant battle, whether this is a private entertainment event or something of newsworthy character ... intermixed with international copyright law.
