So what are we talking about, anyway?
I'm going to try to find Larry Correia's original blog post in which he criticized the trend he saw (and still sees, AFAIK) in science fiction and fantasy (SFF) publishing toward giving preference to works that generally toe the left-wing line and, for extra points, are written by authors whose personal identity (race, sex and sexual 'orientations', ethnicity) place them in a left-wing favored 'victim group'. In it, he included a little cartoon of himself making a plea for a return to intrinsic merit and fun in SFF, which he somehow connected to helping the plight of sad puppies. (I'm not describing it adequately, but it was very funny. The artwork would have gotten a C when I was in first grade.)
There is no "official" Sad Puppies organization, just a lot of people who are sympathetic with Larry Correia's complaint and those of bloggers like Sarah Hoyt and John C. Wright who chimed in with him. Because of the inherently loose nature of the group, there isn't any clear, bright line defining what is and what isn't a Sad Puppy work or author. I myself am not affiliated with any of the organizers of the Sad Puppies 4 web site (though whatever slight contact I've had with them has been friendly), but I'll describe what I mean by calling SFF works and authors Sad Puppies.
The complaint Sad Puppies have about how SFF has evolved since the heyday of giants like Heinlein, Asimov, Brackett, Burroughs, and Clarke is that, whatever the politics of the author and whatever their identities, they wrote stories that were fun to read. Sometimes the stories made political points about the issues of their day, like Asimov in "The Martian Way". Sometimes they were hostile toward religion, like Burroughs in The Gods of Mars. But they never figured that getting in their digs was a substitute for telling a good tale. They didn't write to assure their readers that their opinions were the "correct" ones and then expect praise for it. They didn't write to deliberately cajole like-thinkers and drive off dissenters. They didn't write propaganda.
So a Sad Puppy work, as I use the term, is a work that (1) is fun to read, and (2) is either not "message fiction" or at least does not make readers who disagree with its message reasonably conclude that the author hates them and would rather they went away and read something else.