The author's thesis is that the real benefit, to average and gifted kids alike, is not having to be in the same class as the bottom rung of kids.

I find that thesis at least plausible. I went to regular public school for K-8, then a magnet school for 9-12. It's really the bottom 10%, usually kids with behavioral or social problems, that makes the experience worse for everyone.

At the same time, I'm not sure my magnet school experience would've been appreciably worse with a bunch of average kids in the class. Maybe the teachers would have had to teach the material more slowly and we would've covered less of it, but the fact is that very little you learn in K-12 matters anyway.

And herein lies the problem with K-12 for gifted students. Why should kids be learning things that don't matter when they are capable of more?

(Note: I disagree with the claim that little in K12 matters; every bit of knowledge lays the foundation for the next layer of abstraction. E.g. counting->arithmetic->algebra->calculus/statistics, or alphabet->spelling->vocabulary->grammar->reading->writing->essay writing/research.)

I disagree. Most of what is learned in K-12 is foundational for things learned later (literacy, numeracy, and basic social skills at the earlier grades, more developed hard and soft analytical and communications skills in later grades.) Even to the extent that the nominal subject matter may not be particularly generally useful later, it tends to serve as a focus for more generally applicable skills.

Some variant of academic socialism?

Could it be packaged with social socialism for the gifted kids who lack in other social areas?

Also, the argument isn't that gifted students are responsible for pulling up peers. The argument is that by being around people like that, it benefits others. Much like integrating schools and having different income levels in the same school helps others.

Unless you have a special gifted program, that's generally only true in high school and maybe middle school, and (even then), is subject to the availability of distinct "upper level" classes, which even in high schools may be limited in districts where the effort is focused on maintaining the middle and bringing up the bottom.