This is an extractive summary: it scores every sentence by how many of the article's most frequent meaningful words it contains, gives the opening lines a small bonus, then returns the top scorers in their original order so the argument still reads in sequence.
Extractive summaries never invent a claim the author did not make, which is their real advantage over generated prose. The trade-off is that a poorly structured article produces a poorly structured summary — garbage in, garbage out still applies.
Use three sentences when you only want to decide whether the piece is worth reading, and six to eight when you want notes you can keep instead of the original.