> Removing the filler "uh" the sentence becomes "Like their purpose." Which could be semantically understood as "[I/He/They] Like (or enjoy) their (whale's song) purpose." A semantically ambiguous sentence is just that, ambiguous. This sentence can have multiple meanings.

Your argument supporting your prior assertion that "the sentence has meaningless grammar/syntax" is that... if you remove part if it, the sentence ceases to make sense?

Their sentence isn't semantically ambiguous. You may not understand the meaning of their sentence, but your experience is not everyone's experience. The word "uh" in the quoted sentence serves a particular purpose--it's an emphasis of the ridiculousness about how little we know with respect to the animals. Moreover, it's a very concise way of communicating that emphasis.

If anything, the fact that removing “uh” changes the interpretation is solid proof that it is not semantically empty.

It adds emphasis. Translated: “Like, even their purpose!”