Think about it, the words behave like genes. Strongest words survive. Words mutate, combine, and cross. Words evolve. And we, people (with all our information carrying devices), are their environment.
This is more a question of semantics than a question of philosophy. Most can clearly see the similarities and differences between a biological living thing and a language.
But whether we call language a living thing or not is merely to do with how broadly we use the term "living thing" in our speech rather than related to the true essence of "language" and "living things".