I would imagine that it means that the creatures can communicate in their "language" so you understand, limited to their perception of everything. But I guess you could rule that they only hear and understand.
Otherwise, heck, I "speak" to all living creatures. Whether or not they listen or talk back is different.
The preposition "with" gives the meaning of two-way communication. If the intent had been to only allow others to understand the monk regardless of known languages, the wording would have been "speak to".
That being said, I agree with the ruling that in order for the communication to be two-way, the living creature in question needs to have the capacity for verbal communication.