The problem with that chart is that suicides are included...distorts things a bit.
Actually, this chart shows that guns in private hands are as dangerous as any other tool, no more. The relation is nicely linear. Twice the guns, twice the deaths, all along. Just like anything, might be expected. If the popular private gun ownership was inherently more dangerous than, say, chainsaw ownership, we'd see some bending up of the line on the right hand side.
The USA are an exception, so there's something going on there. Now I'd like to see similar statistics, but with the US states compared.
When I was in Poland, I observed how they act when they get really mad at each other after having too much to drink. With guns, I can imagine how those very lively "disputes" would end up.
And how do they end up with knives, choppers, axes, pitchforks, hammers, screwdrivers easily available? Every kitchen has a set of sharp pointed knives, often in full display on special stands, and every house has a drawer full of sharp tools.