It' on Aegean's website, meaning it applies to Aegean flights. On those *G and M+B Gold receive an extra piece of luggage as per *A rules.
In addition M+B Gold receive the same benefit on OA. I think your highlighting is a bit off, let me show you what I mean:

“Miles+Bonus Gold Members* and Star Alliance Gold Members have the right to carry free of charge, one additional piece of baggage.... *The benefit is also available on Olympic Air flights.”

The key thing to note is that the asterisk clearly only relates to M+B Gold and not Star Alliance Gold. This single sentence basically can be split into 2 separate statements:
- M+B Gold and *G receive one additional piece of baggage on Aegean
- M+B Gold receive one additional piece of baggage on Olympic Air

I can totally understand your frustration. Unfortunately this is what *A has come to, more and more members have non-Alliance subsidiaries for domestic service (LH has Eurowings for instance).
The complication is that domestic flights within Greece are generally OA flights, even though operated by Aegean (wet-lease kind of situation, as explained by KLouis).