First, it's a bit of a silly cliché, but a true one, that guns don't kill people, people kill people. The way you've phrased it, even aside from the facts, makes it feel like FUD implying that someone's gun is going to creep up on them in the night.
Second, you can just take it from the horse's mouth, since papers give you an abstract stating their findings. An even briefer snippet of what they say themselves there is:
> Those persons with guns in the home were at greater risk than those without guns
> in the home of dying from a homicide in the home. They were also at greater risk
> of dying from a firearm homicide, but risk varied by age and whether the person
> was living with others at the time of death. The risk of dying from a suicide in
> the home was greater for males in homes with guns than for males without guns in
> the home. Persons with guns in the home were also more likely to have died from
> suicide committed with a firearm than from one committed by using a different
> method.
The first half of that regarding homicide says nothing about being killed by your own gun, only about being a homicide victim in your own home. It _could_ and likely does include some of that, but it's not captured or quantified, all we see is total homicide numbers. Nor does it have any statistics about anyone else killed, either outside the home, or someone else killed in your home, so there's no basis for comparison there.
The second half only claims to be true for males in the first place, not everyone. It also explicitly acknowledges that it doesn't deal with the likely confounder of people who don't have a means of suicide in the home committing suicide _outside_ the home, and thus not being included in their numbers.