I looked at that page, and the only thing I see is that the number of violent crimes went down between 2009 and 2013.
There is another page at https://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2013/crime-in-the-u.s.-2013/offenses-known-to-law-enforcement/expanded-homicide/expanded_homicide_data_table_8_murder_victims_by_weapon_2009-2013.xls that states that while in the same time frame the total number of murder victims went down 9% (consistent with the overall decrease in violent crimes), the percentage of firearm-related victims went up from 67% to 69%.
Not that this affects your point, I think…
While the fact that, compared to for example Germany, the US has a homicide rate that’s 4 times higher but a firearm-related death rate that’s some 50 times higher, says that people mostly substitute missing firearms with other means, the homicide rate is still significantly higher.
I think there is a cultural issue here, and I’d like to see that more in the center of the discussion rather than limiting access to guns. I don’t own a gun, and I don’t quite see that there is a need to own a gun, but that’s me… In any case, I don’t think that limiting the sales of guns will do much to change the problem. (OTOH, I find it really, really stupid that people have to go through a background check when buying from a licensed dealer and don’t when they buy from a guy at a gun show.)