This has to take the cake for "most spurious correlation."
The most coherent reading is "places which report more homocide data are correlated with reporting more left-handedness"
It could also be that when fighting (pre guns) people with left handed weapons took normal right handers off guard (sort of like how in baseball a leftie might throw off other players). I can imagine in a sword battle if you are used to fighting people right handing swords that suddenly fighting a left handed person could be unexpected and disadvantage you.
Where I am going with this is that it might not be that left handedness directly correlates with violence in any way - but perhaps societies with more left handed people were simply more likely to survive in more war like times.
Yes left-handed advantage is a major thing in combat sports including fencing. IIRC close to 50% of professional boxers and fencers are left handed, which is similar to the rate for pitchers I believe.
Which is still higher than average, and around the level seen in more violent societies. I think it makes sense that it wouldn't get up to 50% since you're sampling from a smaller pool in the first place.
They're also conflating stance and handedness, which may make sense in boxing I don't know much about that sport. But in judo for example there are other factors in stance choice and only about half of left handers mainly use the "left handed" stance, and plenty of right handers prefer it also.
Overall probably just really hard to get good universal data on this. I'm curious about fencing though. Another sport I don't know much about.
I wonder if this is where the whole left handedness being associated with the hand of the devil (or any evil) came from historically. Our ancestors probably weren't doing studies like this but like many religious/spiritual restrictions that seem like they are backed by "nothing" at first turn out to have a fair application to life behind them it's probably not too much of a stretch that someone at some point or other noticed something like hey, that village/tribe/whatever near us has a LOT of left handers and they have an awfully suspicious amount of violent incidents happening.
Study does not exactly imply that left-handers are the cause of the violence, just corelated to societies' total violence. Perhaps we are exceptionally annoying to right-handers. This 'um, actually...' post would then be a salient self-referential sample of what I mean.