Venison is still venison, (who's ever heard of buying "dear meat"?) Chicken was always chicken as a meat, "poultry" refers to the livestock as a collective noun.
I beg you to go to your local butcher (or butcher's counter in your supermarket if you don't have a butcher) and order a kilo of "swine flesh" and see how widespread that usage is!
Whoever wrote the section of the wikipedia article you quoted clearly doesn't speak English as a native language, or was having a joke at your expense.