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It's just a long term licence to watch it
Strictly speaking, so is a DVD or other physical media, per the EULA they flash across the screen for half a second before starting the show and therefore makes it legally binding.
The big difference is that nobody's running around trying to claw back DVDs. Whereas, with Amazon, its trivially easy to just click "Remove License" from the repository and snatch back an arbitrary number of licenses. Purely a question of convenience.
Of course, if you have a... uh... backup copy stored conveniently on a PLEX server, then they can't claw that back either.