... but not less violence, nor less deaths in general. Japan, for example, has some of the strictest gun laws in the world, as well as one of the highest suicide rates. According to recorded statistics, if we assume accuracy, the US is well below the global average homicide rate of 7.6 per 100,000 people, at 4.8. One thing I noted from the aforementioned chart, there doesn't seem to be any correlation between presence/absence of strict gun laws and homicide rates.
Citing "less gun deaths" in countries with strict gun laws is like citing "low auto-accident rates" in Nambia - complete non sequitur.
While the US is well below the global average, it's worth noting that it's well above the average in most of europe. The global average is skewed high due to high murder rates in Africa and South America. From the link you provided:
How much of that difference is gun control laws in these countries and how much is cultural differences is a question to which I don't have an answer. But please, let's compare apples to apples. Being "better than Namibia" (17.2) isn't good enough for me.