The OP makes 2 references to “language”:
As Dr. Beard notes in his article, we must indeed distinguish between language and communication.
Obviously, all animals communicate (even corals, which are hardly recognizable as animals). It can even be argued that plants communicate. And it’s generally accepted that higher animals learn.
But using language is a different kettle of fish. What distinguishes language from systems of communication such as calls and pheremones, for example, is the use of arbitrary symbols with socially negotiated values in conjunction with an underlying syntax to produce completely novel utterances which can be accurately decoded. The power and utility of language is significantly superior to non-linguistic systems of communication.
I do believe there is a “language/no language dichotomy”. However, we don’t need to accept a clearly defined dichotomy for the distinction to be meaningful. It is impossible, for example, to determine an exact altitude where our atmosphere stops and outer space starts, or to define precisely when dialects develop into separate languages – but this does not imply that there is no meaningful difference between atmosphere and space or between dialect and language.
Communicating with one’s fingers isn’t necessarily language. ASL, however, is language. Koko does not know or use ASL. She has learned to use gestures in a way that gets her what she wants, and perhaps to communicate. But she doesn’t use sign language. She doesn’t have linguistic ability.