It kind of depends on how you define mass killing. If we use Smartcookys list of the 13 mass killings that you reference and then filter that by the gun violence archive definition:
and just go with killings rather than shootings.. that trims it to eight (8) mass killings.
If we use the narrowest definition which is:
Now we are down to four (4) attacks.
Whatever way you slice this you're wrong. Ready access to firearms increases the number of homicides and suicides and, most pertinent to this thread, mass shootings.
In 2016
according to here there were four hundred and seventy seven (477) mass shootings in the US. That data is using the "more than 1 person was shot" criteria which looks to be a similar criteria for your list of 13 (which has no entries for 2016 btw)
Though lets stop arguing over semantics.
Now we're getting somewhere.
If we put aside all the extreme points of view I firmly believe that most people in the US agree that there ought to be some further restrictions of firearms in the US.
The US has the 2nd amendment and a long (relatively speaking) history of gun ownership. It's possible to bring in further gun control measures that greatly reduce easy access to powerful guns, while still permitting most of the people access to a lot of guns, which could go a long way to reducing mass shootings (and possibly other homicides and suicides) in the US.
It'll never happen though until everyone sits down around the table and works out the best "common sense" approach.
I'd suggest that both the "cold dead hands" brigade and the "ban all guns brigade" were excluded from such negotiations until they grow up.
In the US and the UK and in Australia the number of homicides and suicides and mass killings is too damn high!
I don't know how we might reduce these figures in the UK. I'm open to suggestions. Increased gun control in the US I think would go some distance to reducing these deaths in the US and bringing the figures per capita more in line with other western nations.
It doesn't have to be gun control like we have in the UK or in Australia, but it'd be a good thing if the policy makers in the US could sit down and talk about some common sense regulations that could be brought in, that would make a significant difference.