Dama dama is native to the region around Greece and Turkey, and possibly to parts of the Italian Peninsula. It was moved around by humans in the Mediterranean a long time ago (starting around 9000 years ago), and introduced into many areas.
It’s easily possible that it’s considered native to Friuli Venezia Giulia, but introduced to the Alps as a whole. The Alps is a much larger region and Friuli Venezia Giulia only overlaps a little bit with the Alps.
There is no real conflict there.
The IUCN range map is a bit conflicted, as they often are, but spells it out decently well. Although it looks like it does not include Friuli Venezia Giulia as part of the native range.
The key for the Wikipedia map is here:
1: (Former) native, includes D. mesopotamica
2: Possibly native
3: Early human introductions
4: Modern human introductions