It depends on your definition of mass shootings I suppose but the 250 number comes from here:
https://www.gunviolencearchive.org/reports/mass-shootingThese shootings weren't all deadly(so there might be a discrepancy there) but they are real incidents.
The guns are used as the tool to enact change because they are the most powerful and practical tools the shooters have available.
When there are no guns available they will just try and use something else like cars or trucks so just banning guns won't solve the issue.
The killer made that clear in his manifesto too, the attack was poorly prepared but the weapon he had was most suitable for the 'wake up call' he had in mind.
That however, still does not mean you should not get these guns out of the hands of people who clearly shouldn't have them so background checks are nothing but common sense
and there is no reason for anyone to walk around with an AK47 and a drum magazine.
Anyhow, this ideology is not clearly defined like ideologies of the past like Nazism, Marxism or Islam. It is closest to the stuff you find in a game like Deus Ex or any other fiction about the end or control of society.
Similar to that sort of fiction it is just a zeitgeist accumulation of news media, pop-culture topics and current world affairs that formed an ideology in their minds but doesn't really exist.
However, on a daily basis they get fed enough images and commentary that allows for their confirmation bias to kick in and accept their own mental creation.
This cynical doomsday view of the world is pretty much real to them. Look no further than say a place like NeoGAF or ResetEra where some posters already show the same signs.
