A literary magazine that focuses on a particular genre of fiction. These typically publish short stories and novellas, but sometimes serialize longer works. (e.g., Dune was serialized in Analog magazine.)

The blogger, Neil Clarke, runs a science fiction genre magazine called Clarkesworld. Other science fiction genre magazines include Asimov's, Analog, and F&SF.

Other genres, including so-called "literary fiction," all have their own magazines. Apparently none of them are doing particularly well, because short stories are now out of fashion. The trend right now is to make everything as long as possible: Don't write a novella if you can write a novel, and don't write a novel if you can write a three-part (or seven-part!) series.

"Genre" here means genre fiction https://en.wikipedia.org/wiki/Genre_fiction, the sort of mass-market books like romance, fantasy, science fiction and horror. Compare with literary fiction like classics and poetry. It can be used derogatorily to separate commercial literature from "real" literature since genre fiction were usually printed on cheap trade paperbacks, sold in volume and read for entertainment compared to more serious literary and artistic fiction, but I don't think many people today would make that distinction.

I think they mean something like say, Lightspeed Magazine is a genre magazine, and the genre is scifi.

However, we seem to have saturated their database connections (friends don't let friends have connection pools without bounds/with the wrong bounds, especially not to serve static content), so I haven't read the article. [ETA: Did read it, am now positive.]