Apparently, Milan's show is also popular in Russia, where it's called Переводчик с собачьего -- which basically means "The Translator Who Speaks Doglish".
More literally, it means "Translator from Dog (language)" -- the word языка is logically understood but not used. And "собачьего языка" is in the genitive singular, because as I mentioned in your "shoes" thread, one of the functions of the genitive is to indicate "away from." In the case of translations, one goes "away from" the source language (genitive) and "into" the target language (accusative) -- с французского на китайский (from French to Chinese), or с собачьего на человеческий (from "Doglish" to "Humanese").