I first heard about this from the autotldr bot on Reddit [1] which uses a similar service SMMRY [2].

The SMMRY page points out some extra NLP-related grunt work in addition to the high-level steps you list, like:

>Associate words with their grammatical counterparts. (e.g. "city" and "cities")

>Detect which periods represent the end of a sentence. (e.g "Mr." does not).

[1] https://www.reddit.com/r/autotldr/comments/31b9fm/faq_autotl...

[2] https://smmry.com/about