As an amateur who's been fascinated by this puzzle himself, I will add some context that might be relevant in assessing the plausibility of this claim:

- The "Libation Formula", which the author used as the base for his translations, is the most studied piece of writing in Linear A, because it's the only recurring phrase (with grammatical variation) that we have. The corpus is extremely fragmentary, with just a handful of instances of longer text (and even then, the texts are the length of an average sentence in English). The majority of documents available to us are lists (of inventory, personnel, offerings or something of this sort). The longer texts make use of punctuation marks, likely put in between words. This gives us a non-trivial vocabulary, which still does not match that of any known language.

- With such fragmentary remaining material, we cannot be sure that a) all the texts we call "Linear A" are written in the same language, and b) the recognizable words are not abbreviations, for example.

- The author made an assumption that Linear A symbols which have counterparts in Linear B should have the same phonetic values. This gives us an already known glyph that represented "NA". "Duplicate" glyphs are only found in the P-series, and are assumed to represent syllables which were distinguished by the Linear A language, but not by Greek - such as aspirated/unaspirated P. There is a glyph that stands for "NWA" in Linear B, but instances of it have been found in Linear A as well.

- There are countless words with no known etymology in Ancient Greek, assumed to originate from a substrate language or languages spoken in the area at the time Greeks migrated to their present-day homeland. The language of Linear A would be a likely candidate for such substrate. If Linear A were a Semitic language, then we should already be able to establish Semitic etymologies for those words as they were in Greek. Of course it could also be the case that these words came from an another language which did not adopt writing or its writing did not survive to our times.