Mycenaean Greek is an Indo-European language. Hebrew is a Northwestern Semitic language. This by itself makes the notion a non-starter.
Gordon makes the case in the book that Minoan and Hebrew have the same roots, and Minoan culture preceded the adoption of Greek in Mycenaea in his speculative Eastern Mediterranean civilization, but this is unfounded in science - as Minoan remains untranslated and unclassified. If it were as closely related to Hebrew as he claims, it would be translated or at least classified into a language family by now by tracing back language features to Northwestern Semitic or its precursors in the Afroasiatic family.
In short, Gordon could not prove Minoan was related to Hebrew in any meaningful way. Without a shared language, it's unlikely the cultures developed from the same source.
More, he was invested in other questionable historical beliefs that receive regular debunking - such as precolumbian trade with the Americas by many of the ancient Mediterranean civilizations.