For starter they do not have a global model, it seems that they handpicked different statistics for different areas that support their thesis (they do not even show anything concrete for Japan).
Regarding Sardinia, their numbers seem actually wrong: looking at the raw Istat data the numbers for 55 year life expectancy for the Sardinian provinces seem in line with the rest of Italy (95-96%) putting Sardinia somewhere in the middle of the (quite tight) Italian distribution.
It is possible that the researcher averaged the data over a longer period of time that I bothered to look is possible, but the paper doesn't discuss the methodology.
Their fitting, p value not withstanding, also seem a bit adventurous; the fact that all and almost only Sardinian provinces are extrme outliers shoud have been a tell. The rest of the Italian bprovinces are in a tight uniform cluster.
Sardinia, except for a very brief period in the mid 2010s,has only 4 provinces, so it is possible that messed up their data extraction (they show 8 provinces).
Also Sardinia is not particularly poorer than the rest of Southern Italy and actually has a lower crime rate (which they suggest but not outright state is a factor).
A better paper would probably try to build a single model for Japan, Italy and US using actual mortality, crime and poverty rates.