Nice! I find myself wanting to say "no, surely that just means that they refuted one particular sort of semiclassical gravity" but I'm not sure what other sort there might be.

Still, for me the main conclusion is: Yup, semiclassical gravity is wrong, just as we already knew it to be. More specifically, surely no one expects semiclassical gravity to be a good enough approximation in situations where the distribution of mass is made appreciably "different in different branches" (I don't mean to presuppose Everett here, it's just the easiest way to say it). So this experiment is finding that semiclassical gravity isn't a good approximation in situations it was never expected to work well in; blaming that specifically on the Everett interpretation seems perverse.