ContentID, versus a company not knee deep in the consumer video industry.
While Amazon may not have a YouTube competitor, they certainly have a consumer video product in Amazon Prime Video.
Twitch already rolled out their own ContentID-styled system, pre-acquisition.
Pre-acquisition announcement! The timing of the two is so similar I think it's beyond likely that the anti-copyright protection wasn't a part of the negotiations.
Amazon is in the music and video industry. Twitch already has content ID. Amazon is pretty much Google-level evil plus sweatshops.
Something no-one else seems to have mentioned in response to you is avoiding monopolies. Various changes to youtube regularly piss off people uploading content to the platform, so having a competitor (twitch) gives them somewhere to run to, and competition in the video market.
Amazon sells actual products to consumers, Google sells consumer data to advertisers. That means Amazon tends to be more responsive to end-users.
As an experiment: Compare trying to get somebody from Google support on the phone vs. Amazon.