I'm glad to see that rational people are looking at the data and formulating hypotheses based on some evidence, as opposed to just making blind conclusions.
The null hypothesis based on the links you've shown us might be that more guns associates with more gun violence. Perhaps there is other data that exists that does not show that association. Perhaps there is data you missed that might refute what you're implying.
But the old correlation/causation bit must rear its ugly head here. We don't know why more guns MIGHT lead to more violent gun crime*. After all, the guns can't shoot themselves. I would like to see more research done in this area.
We can't just create additional restrictive gun legislation, dust our hands off, and think we've fixed the problem until we know the "why." I don't think we'll ever know "why" these horrific events occur.
But we do need to be more stringent with our research if we are going to hypothesize that more legally-owned guns associates with more violent gun crime. This is, after all, what many liberal politicians and citizens alike are talking about (reducing the number of law-abiding citizens from legally obtaining firearms). To do that, we need a retrospective analysis of violent gun crime comparing two or more populations with diametrically-opposing gun laws. You would then have to exclude from that analysis incidents of defensive use of a firearm (ie. personal and home defense scenarios). Then, I think, you would also have to exclude incidents wherein illegal or unregistered firearms were used. If you want to create new gun legislation barring citizens from legally purchasing or using firearms, you should have some data showing that citizens using legally-owned handguns are committing violent gun crimes that are not defensive in nature, and that there is a significant difference between the population with the "lax" gun laws and the population with the very restrictive gun laws. Basically you would need to prove that gun control legislation stops people from using legally-purchased and legally-owned firearms to commit violent gun crimes.
Although this imaginary research still wouldn't tell us "why," it would certainly be much more compelling than the data you've provided. We could put a little bit of stock into the associations we find, if indeed we do find any. Even then, it wouldn't be compelling enough to further restrict our Second Amendment rights.
*We don't know if that's even true because one could certainly cherry-pick and data-dredge to tease out all kinds of correlations and support almost any hypothesis.