That's quite a sentence! Right off the bat, let's acknowledge that it's a bit ambiguous or at least confusing, and could have benefitted from rewording. I'll make an assumption that it means that all the essays by all the authors are both readable and dated, and analyze it accordingly.
To break it down, let's imagine how the author might have built it up from simpler beginnings.
Jack's essays are still readable.
"Sure, but they're kind of dated. I'll add a dependent clause."
Jack's essays are still readable, though somewhat dated.
"You know what, this describes the essays by Braybrook and Hollis—'still readable, though somewhat dated.' I'll mention that."
Jack's essays are still readable, though somewhat dated, as are those by Baybrooke and Hollis.
[Editor's note: At this point the author took a bit of a misstep, since this could be taken to mean that B & H's essays are only "dated," not "readable." I'm pretty sure the author means both, though.]
"In fact, 'readable but dated' describes Baybrooke's and Hollis's essays even better than Jack's. I'll add another dependent clause."
Jack's essays are still readable, though somewhat dated, as, to a greater extent, are those by Baybrooke and Hollis.
And there's the structure of the final version (with a few adjectives still left out). We have a dependent clause, "as are those by...", itself interrupted by another dependent clause, "to a greater extent". Note, the author could have put ", to a greater extent at the end of the sentence instead.
As noted, though, the sentence is so convoluted that it's confusing, and the reader might consciously or unconsciously think that "... as are" modifies only "dated," not "readable" as well. (Or maybe the author did mean only "dated," in which case it's even more misleading.) What might be a good rewrite?
Jack's various essays from the 1950s are still readable, though somewhat dated. Those by Neville Braybrooke and Christopher Hollis from the same decade are even more readable, though even more dated.
Update: After reading Colleen's take, I'm not at all confident that what I wrote above is the only interpretation supported by the grammar. Hopefully the context makes it clearer. Why is it so difficult? Let's once again imagine a simpler sentence:
Ms. Smith is strict but fair, as is Mr. Johnson.
Here, "but" is a coordinating conjunction; both "strict" and "fair" equally describe Ms. Smith. It's reasonable, then, that the "as is" applies both to Mr. Johnson as well.
Ms. Smith is strict, though occasionally kooky, as is Mr. Johnson.
Here we have the ambiguity that was present in the original example. The main verb and object of the sentence are "is strict," and "though occasionally kooky" is a subordinate dependent clause. To be honest, I'm not sure at this point whether strict grammatical analysis gives any ruling on whether "as is Mr. Johnson" must modify "kooky" or "strict," or both. Common sense would lead us to choose "kooky," simply because it was last mentioned.
If the author intended the B & H essays to only modify "dated," an absolutely horrible rewrite that makes the sentence even more convoluted but more clear might be:
Jack's various essays from the 1950s are still readable, though (as, to a greater extent, are those by Baybrooke and Hollis) somewhat dated.
But much better would be to split up the sentence:
Jack's various essays from the 1950s are still readable, though somewhat dated. Those by Neville Braybrooke and Christopher Hollis from the same decade are even more dated.
