What a strange statistic to calculate. Particularly considering that many of the guns in the US are in the possession of a small number of people, who own umpteen guns each. Not at all sure that it is a particularly meaningful statistic, given that point. Someone with 30 guns isn't going to kill themselves 30 times over, and even a spree killer is likely to only get any effective benefit to their killing rate from 2 or 3 at most.
I would expect the killings-per-gun to be lower in the US due to the sheer number of guns that are held as part of large collections, merely out of a compulsive collecting impulse, and never used. But the existence of those 'display pieces' probably does increase the flow of guns into the criminal market (due to thefts and dodgy sales).
On the other hand, even though it seems a very dubious stat, it's still data, and possibly there's something interesting in there somewhere.
Curious that the gun suicide rate in the UK is so low, even when expressed per-gun. Brits just don't go out that way, apparently. I wonder if that's partly cultural, that different cultures have different traditions of self-annihilation?
The mention of Serbia brings up a tangential thought - that there are a lot of guns in the Balkan countries, and Schengen makes it much easier to move those guns to the rest of the EU. And if Kosovo or Serbia join the EU that issue will get worse.
Another point is that as far as I am aware, France doesn't have particularly strong gun control anyway - nothing like the UK. Not all European countries are the same in that respect.
I wonder why Ireland is so high in that table? Does it have a lot of gun deaths, or do Irish gun-killers just get a lot of use out of the few guns they have? I wonder if that's due to a lot of the guns in the country being in the possession of a few criminal gangs? Or is it isolated farmers wielding shotguns (so tempted to add 'while drunk', but that's probably unfair stereotyping).