Okay, I'm going to take a stab at my own question.
Nonbuddhism is a type of "Critical Buddhism" reminiscent of Japanese "Critical Buddhism". It appears to be a reform movement that is highly critical of a variety of elements in modern Buddhism. Unlike the Japanese version of Critical Buddhism, nonbuddhists (or at least Glenn Wallis) seem uncertain if anything will be left of value after removing the objectionable parts. The Japanese "Critical Buddhists" on the other hand, seem to want to remove a particular set of ideas they find unbuddhist.
Another distinctive part of the approach is mixing in modern Western philosophers. The name non-Buddhism is from Laruelle, who describes philosophy in a sort of "shadows on the wall" metaphor, where all philosophies are a project of what philosophy really is (which Laruelle confusingly calls non-philosophy). So non-Buddhism appears to be trying to recover what Buddhism really is from examining all the other Buddhisms.
Glenn Wallis previous wrote what were scholarly, mostly secular Buddhist books (and by secular, I mean, in the same family as Stephen Batchelor, pali centric and not interested in the reincarnation, karma, etc)
Tom Pepper is a Shin Buddhist, whose ideas overlap with Glen Wallis, but also clearly wants to integrate a Marxist viewpoint into Buddhism.
If anyone can fix up my answer by posting their own, that would be great.
Okay, I'm going to try to include the content of some of the other answers here, since some of those answers are getting self deleted and downvoted for, what I suspect is their combative tone and obscurantist literary style. Not saying it's bad, just calling spades spades.
Non-Buddhism is a sort of methodology. The proponents aren't so much as coming up with a new list of orthodox beliefs but a means for people to transform the existing materials of Buddhism into something better.
Non-Buddhism entails a sort of particular dialectic, in the sense that to find truth, people should take up propositions and defend them vigorously, dispensing with social niceties, especially Buddhist social niceties. What comes to mind from the Buddhist tradition are the stories of eccentric Zen masters breaking arms and killing cats to make a point, or Shambhala style "crazy wisdom"
Non-Buddhism entails an ontology that roughly says, things are irreducibly complicated, the topics under discussion can't be simplified. Despite this, they don't seem to be arguing for a Mahayana view that certain parts of Buddhism are beyond (ordinary) comprehension, just that Buddhism requires what looks to me to be about a graduate degree to accurately work with Buddhist ideas.