Linguistics as a discipline clearly does take Damin and Ge'ez to be part of its legitimate subject matter. So if we've defined "linguistics" in such a way that Damin and Ge'ez are ruled out, then I'd argue we've got the wrong definition.
My sense is that the descriptivist/prescriptivist line is the right one to use. This would have the consequence that we'd have to accept descriptivist questions about Esperanto. But I don't see the harm there. If someone has a legitimately descriptive question about Esperanto — for instance, "Which word order do real-world Esperanto speakers use most in spontaneous face-to-face conversation" — then I'm totally fine with that. (And honestly I think most working linguists would be too. If a student in my department wanted to do fieldwork at Esperanto conventions for their dissertation, I don't think anyone would bat an eye.)
The real problem with Esperanto is that most discussions about it aren't descriptivist. The question most commonly discussed isn't "As a matter of descriptive fact, how do Esperantists actually talk?" but rather "How should Esperantists talk?" and "Why is Esperanto better than Lojban?" and so on. We should definitely exclude those questions. But we would exclude those questions even if they were about natural languages: "How should Anglophones talk?" and "Why is English better than Spanish?" would be deleted just as quickly. For that matter, "Why is Damin better than Lardil?" would be deleted. It's a single consistent standard we can apply across the boad.
Similarly, if a conlang has never had a substantial community of human speakers, then you can't do real linguistics on it, because there's no human verbal behavior there to study. Even if a conlang does have human speakers, discussing its written grammar isn't linguistics, because it's focusing on a prescribed standard rather than on actual usage. But if someone wanted to know, like, "As a matter of descriptive fact, how do Klingon speakers at sci-fi cons tend to articulate the phonemes /q͡χ/ and /q/?" then I'd be perfectly happy to see discussion on that point. (And again, if a student in my department wanted to do that research, we'd be perfectly happy to give 'em a degree in linguistics at the end of it, so long as they did a solid job with the evidence and argumentation.)
I realize I may be an extremist here, but I figured I'd put my two cents in.