"Not just Einstein, but Maxwell and others."
I didn't understand half the letter. But it's argument was that gravity and "light" (massless particles) dodn't propagate at the same speed. That's undoubtedly weird, but not necessarily fatal.
And while the author argued it was light that was faster, I saw nothing to say it couldn't be gravity that was slower (it's all relative...). Slower gravity is plausible if gravitons self interact -- they would naturally find the earlier universe stickier than the present day one.
So I read this as yet more evidence we don't understand gravity. Which, yes, means more problems for Einstein (cf dark matters vs MOND). But Maxwell, in as much he survived being mugged by Dirac and Feynman, is fine.