The term "Language" on Erfworld refers to a language that is commonly spoken at least by some members of all sides in the geographical vicinity of Gobwin Knob. "Language" is similar to English on Earth, and more closely similar to Common in Dungeons and Dragons. Not everyone on Erfworld speaks Language. For example, Vurp informs Parson that not all the Hobgobwins who live in Gobwin Knob do so.
Since Units pop as adults, they are all created knowing at least one language. The fact that they are not all created speaking the same language is probably a feature deliberately designed into the system by the Titans. If each non Capital side has its own language, this implies a greater degree of cultural diversity than was previously apparent. It's also possible that having their own language makes it easier for a side to keep secrets from other sides. It's possible that Thinkamancers can't read the mind of a unit if it's thinking in a different language.