(the author also writes about exceptions, but they merely prove the rule, so don't challenge the idea of a "ban" -- I just don't understand what is banned).
For the most part, 肉 (niku: meat) refers to mostly land animals and in context, the ban was to discourage the consumption of domesticated animals and game which would invite pestilence and strain on limited space for agriculture. Eating meat in Japan is still kind of impractical, there just isn't that much space, and it pollutes a lot. Lookup how much water, alfalfa, acreage and methane output is required just to breed a single cow.
Fun fact, English and Latin is kind of similar in the meanings of 'meat' and 'carne' with regards to religious diet.