It does mean that it's very strange that every single member of the Klingon military a decade later is, without exception, a victim of the Klingon augment virus. "Remain Klingon" means that those defective victims would not be allowed the honor to serve. Normally I'd assume it's some sort of punishment for the augment Klingons but then in the context of Klingon culture where serving in the military is a great honor, it's obviously not a punishment. So I don't know what happened between Discovery and TOS that led to that.