First off, the "researcher" is David Hemenway, who has been taking money from the Joyce Foundation for nearly two decades to churn out biased "studies."
Yes, we have more
firearm suicides than other countries because we have
more firearms. To be fair, let's look at the
suicide rates from all causes. We have fewer suicides per capita than just about any other first-world country. That includes many countries that supposedly have a higher standard of living than ours.