Yes, Blinkist and its business of providing 15 minute book summaries is, in fact, legal.
According to their support site, "Our Blinks distill the main ideas and most important concepts from non-fiction books, but they are new, original works of their own, written in our Blinkist style, voice, and format."
For this reason, Blinkist and their services are not considered to be copyright infringement. Think: Cliff Notes but for the modern age.
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