According to the 2011 FBI Uniform Crime Reports...
Rifles account for 3.8% of all gun homicides (2.6% of total homicide) <--- Military-Style Rifles are only a portion of this category
Pistols account for 72.5% of all gun homicides (49.1% of total homicide)
Shotguns account for 4.1% of all gun homicides (2.8% of total homicide)
Unknown account for 19.6% of all gun homicides (13.3% of total homicide)
Gun-Homicides comprise 67.8% of total homicide
"Hands/Fist/Feet" compromise 5.7% of all homicide
To put this in perspective:
Hands/fist/feet killed more people in America this year than "Rifles" or "Shotguns" or even "Rifles+Shotguns" combined. It goes without saying that "Knives" or "Other" weapons also far exceeded rifles & shotguns. And keep in mind that of that paltry percentage of Rifle-related deaths, Military-Style weapons are only a portion... so "assault weapons" killed even fewer people. By and large, rifles (especially military-style rifles) are NOT the problem with gun crime in America - that would be handguns. The findings in the OP only serve to reinforce the FBI data. As the OP states, assault weapons do not make a majority part of the gun demographic... so it logically follows that they don't make up a significant portion of the gun-homicide either. Said otherwise, assault-style rifles are not the problem... for every one rifle murder (all types of rifles inclusive), there are nearly 40 other-gun related murders
The only reason politicians rail against "assault weapons" is that it's an easy target. It looks menacing and scary and fearful people vote like idiots. If you look to the Assault Weapons Ban (even a magically 100% effective AWB) as some sort of solution to anything but a fraction of the death guns caused every year - you will be sorely disappointed.