Read the actual research, not the BBC one-line summary.
Since MUP came in, alcohol related deaths have increased in Scotland. Ignorjng the inflation costs etc, the policy has failed on its own terms. The hardcore alcoholics will miss food, stop heating and so on to keep drinking.
Overall consumption (ie social drinking) is down a bit.
So...where does the headljne "13% fewer deaths" line come from? Simple. Since MUP, deaths due to alcohol in North East England rise also, and at a slightly faster rate than in Scotland. That's it. It was all extrapolated from that one comparison.