It's a deep type of sci-fi that deals strongly with concepts--something to make you think. Although I have read other stories that I have very much enjoyed, they haven't engaged me as much as this type of writing.
To answer your original question of "What type of Sci-fi is this?", I'd call it "The Good Stuff", or "Good SF" (to broaden it to "speculative fiction").
As far as printed SF goes, have you seen the anthology "
The Science Fiction Hall of Fame, Volume One, 1929–1964"?
Short stories, they're all good. Highlights that I remember from my youth as a new SF reader are “First Contact”, "Microcosmic God", “That Only a Mother”, “It's a Good Life”,“The Nine Billion Names of God” and “Born of Man and Woman”
Also
The Science Fiction Hall of Fame, Volume Two, novellas.
From Volume Two, my favourite is
Vintage Season by Henry Kuttner and Catherine L. Moore (under the joint pseudonym "Lawrence O'Donnell"). The rest of the titles aren't really burned into my memory as with Volume One, but are still pretty good.
Both of those should be in any respectable public library.