Not sure what those screen shots are saying.
The fact is that as a Star Alliance Gold member - the equivalent of SkyTeam Elite Plus - you can access a lounge for domestic-only flights (with the exception of UA card holders on UA domestic flights). So, if Alitalia moves to M&M, your SEN card will give you lounge access on any Star Alliance flight. You fly Denver-Idaho Falls on UA, or Chengdu-Lhasa on CA, or Auckland-Wellington on NZ, you have lounge access, with a guest, irrespective of the class you fly.
Oneworld is the same.
Comparison: for SkyTeam ElitePlus, lounge access is only on international flights or domestic-connecting-to-international flights. So as a FB Platinum flying Salt Lake City-Idaho Falls on DL, Shanghai-Wuhan on CZ or Jakarta-Denpasar on GA, you do *not* have lounge access.