While archeaological anthropology is always speculative in the regards of ritual, there's still a general consensus that even our paleolithic ancestors honored their kills (the ones who've given their lives so that you can live) through the 'magic' of mimic and illustration. Funny, even humans with a small percentage of our brain power~perhaps not even bi-cameral~were able to understand and appreciate an animal's sacrifice, even if it was just their central nervous systems suggesting the honor/ceremony.
That's pretty much how I see the site's plea, they're never gonna change meat eaters to vegetarians, they (as well as myself) simply would like to see humane treatment of these animals and they're using agitprop to make their case.