I think Collingwood would defend (at least a qualification of) that statement of Wittgenstein's if asked about it. He readily admits that some communication between humans and other creatures is possible, but he thinks human languages tend to be somewhat incompatible with each other: "the assimilation of one kind of experience to another goes smoothly for a time, but sooner or later a break comes, as when we try to represent one kind of curve by means of another" (the unstated premise in this quote being that different cultures have developed different languages, each expressing the emotions common to that particular culture). If true, it's likely that one would hit a communication barrier with a lion much soner.

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"This ‘sympathy’ [= the kind of phonemonon when panic would spread non-verbally through a crowd] (the simplest and best name for the contagion I have described) exists visibly among animals other than man, and between animals of different species; notably, for example, between man and his domestic animals. A dog will snap at a man because it is afraid of him; and the best way to make a dog bite you is to feel frightened of it. However successfully you think you are concealing your nervousness, the dog feels it; or rather he feels the nervousness in himself which he has thus caught from you."

You understand some of what your cats mean because you learned it using the same language games Wittgenstein describes. Also they co-evolved to work with us. But just because you understand three moods of your cat, doesn't mean you would understand their language (if they had one). In fact, it is well studied that cats communicate differently with other cats than with humans.

Sidenote: grouping together non-verbal communication and language fails to take into account the richness of language.