Has this been peer reviewed? A $3 ebook doesn't provide much confidence. This is presented like various other fringe theories, pointing out obvious apparent weaknesses in mainstream views due mainly to sparse evidence, and then not making clear or strong arguments in favor of the alternative. The basic ideas here seemed possible until I got to the paragraph mixing up etymologies and the origins of letters. A sure sign of a linguistic argument going off track (and quite likely being baseless to begin with) is when sound symbolism is introduced. Admittedly that's not quite what's going on in that paragraph, but when it says "proving" that's where I gave up on it.
Furthermore, even if some of this is correct, the conclusions are not necessarily warranted. There are likely some Indo-European-internal influences on how the Phoenician script was adapted for Greek, and that is entirely compatible with the core of the traditional explanation. Or even at the other extreme, the situation could be more like what happened with the Cherokee script, where the shapes and use of letters were based on how they were used in Phoenician but not actually by someone who understood Phoenician-- then again, that's implausible from a historical perspective, because there was plenty of contact and trade or academic interaction between the two groups as I understand it, so there's no need to recreate it. (In fact, that could also explain why Linear A or B was not more successful for writing Greek, if Phoenician instead took over.) I am also quite unclear about what the book is claiming: Phoenician seems quite clearly related to its Afro-Asiatic ancestry (Ancient Egyptian hieroglyphs), so is the book just claiming that any similarity between Phoenician (and by extension Arabic, Hebrew, etc.) and Greek is coincidental, or is it instead claiming that Phoenician is actually based on Greek. The first seems unlikely, and the second has a fundamental problem: Indo-European writing is quite unique in being alphabetic in contrast to many syllable-based writing systems elsewhere (either true syllabaries or abjads like for Semitic languages). The story of how an abjad became an alphabet when adapted by the Greeks makes sense-- it was an accident, a mistake, and they ended up with vowels. Explaining how that happened, unlike all other attested cases of orthography development, without going from abjad to alphabet, doesn't seem likely: an Indo-European internal explanation relies on the idea that somehow they were targetting an alphabet to begin with, unlike other examples of writing developing around the world, or that they happened to make the same mistake/leap that is otherwise attributed to Phoenician. From a cultural perspective, it also seems obvious that somehow the development of writing in the region was all connected to some degree, even if the individual scripts were to varying degrees distinct. The number of questions introduced in this summary is far more than the number it suggests answers to, so I'm left skeptical and unconvinced. Perhaps that's just in the presentation of the summary.