Even if we do a massive goalpost-move and grant that the system is only identifying the label "dog" with a brain scan of a person looking at a dog, we would need to see actual statistics of its labelling accuracy before judging it in that way. If the images in the paper are cherry-picked(1), it could easily be only able to extract a handful of bits to no bits at all, and the entire thing could very well turn out the be replicable from random noise.
(1) Note that the paper even states "We generated five images for each test image and selected the generated images with highest PSMs [perceptual similarity metrics].", so it even directly admits that the presented images are cherry-picked at least once.