The phrase we are talking about is "handgun deaths," to compare apples to apples (that is what that poster is talking about). It's meaningless to say that there are "only" 6,371 handgun homicides in the context of what the poster is referring to, because it's including only a smaller subset of a larger number. Apparently nearly 20,000 people killed themselves with guns in 2010 -
http://www.pewresearch.org/fact-tank/2013/05/24/suicides-account-for-most-gun-deaths/ - and I would have to assume the significant majority of these involved handguns. My point is that it's misleading to compare homicide-only numbers for recent years to "handgun deaths" numbers from the 1980s and argue that the number has gone down - in fact it has risen considerably.
I am not anti-gun - I am a gun owner myself - but this kind of fast-and-loose-with-the-facts argument inhibits real productive discussion in my view.
(Also, as an aside, I do think it's fair to include suicides in overall gun mortality numbers, since guns are so much more effective as a means of committing suicide than other methods - this is why the success rate of suicides among men is so much higher than it is among women.)