No, the Greek sphinx, from the riddle and Thebes and such. They aren't related creatures:
It's actually not clear to me when the Greeks first applied the term Σφίγξ to the Egyptian one, but it seems very late—all of the mentions before the Hellenistic period that I can find (and actually also in, like, Pausanias) are all about Greek sphinxes. This doesn't absolutely rule out that the word originally referred to the Egyptian one before it came into Greek, but it definitely moved in the other direction later.
The variation in the Greek Beekes lists at least possibly suggests a loan from a language with a prenasalised velar, like many other substrate words:
And it also has the "Pre-Greek s-mobile". If you buy into Pre-Greek in the first place, then this is a fairly obviously Pre-Greek word. If you don't, it still looks like a substrate word and not particularly like Egyptian.
(I actually don't think all of these variants are necessarily the same word, and I think the monkey ought to be separated out from the sphinx.)
But he does mention an Egyptian etymology! He refers to a "Mac Creedy" in Glotta 46, which is actually A. G. McGready somehow. The article is Egyptian Words in the Greek Vocabulary, and here's the relevant passage in full:
I don't know who Gunn is (it's the only time he's mentioned in the article and there's no bibliography that I can see), but it's not clear that šzp-ꜥnḫ (as opposed to just šzp) ever did refer to the Egyptian Sphinx, and we have no idea what the vocalisation would be. It's not a good etymology!
I don't want to defend Beekes too hard, but apart from mangling McGready's name this is not particularly egregious behaviour from him.