He doesn't mean to say the conversation is meaningless, just that the signs themselves have no intrinsic meaning, since they're arbitrary. Which, duh. It's a banal claim articulated poorly.

There's a little bit of ore here to mine (there are philosophical accounts of natural meaning, for example; see Paul Grice), but he mostly seems to just believe in a transcendental signified, and missed the boat on how incredibly rich the consequences of e.g. J. L. Austin and late Wittgenstein are for how we think about language.

Speech by being is one thing, but words on the page have little hope of cohering semantic. This isn't theoretical physics, this is the transition of syntax from the writer (the task variable meanings that are no longer specific, they are arbitrary) into grammar/metaphors, beset by a paradoxical condition called conduit metaphor that dissolves access to that initial mental state, and lets the meaning run wild. Additionally, In functional linguistics, because the status, control, bias, manipulation, ie social elements are quite separate from the agentic, the dark matter of this warps access to meaning. Keller is a best case hypothetical. When we run long segments of text, you ask 20 people you get twenty meanings. So, yes, language is meaningless: it's arbitrary.