Sorry to resurrect this thread, but even though in the past things worked smoothly as malmostoso wrote above, unfortunately I have to report that just two days ago I was denied the loading of luggage for *G on a AirDolomiti Light fare.
I was at MUC for a MUC-BLQ flight.

I asked to talk to a supervisor, and she also insisted that "one additional piece" for *G does not mean what I think it means. However, the supervisor was from LH, not from AirDolomiti, she had printed rules (in German) from the LH website and she insisted that LH rules supercede AirDolomiti rules even on an flight operated on a AirDolomiti ticket on a AirDolomity plane.
Anyway, she used her authority to deny the loading of my luggage (a small 12kg baggage) so I was forced to go to the excess luggage desk.

In the end it was a frustrating experience and a net loss of time and money.
And I still don't understand why LH rules supercede what AirDolomiti write on their FAQs.

I actually had with me a printout of that FAQs page regarding luggage, and despite the clear stating of "one additional piece of luggage" without any reference to the type of fare, the LH employee insisted that "there must be another page explaining that it does not apply to Light Fare", but could not point me to that other page.

I have tried to contact the AirDolomiti customer service for a clarification but no luck yet. And since I have a return ticket, this could mean more pain soon.

PS: my *G is with Aegean of course.