I'm not sure I understand why intent matters (barring accidents, I suppose)?
Who cares what the intent was if guns were involved and people were hurt or died?
If a person is suffering from schizophrenia and thinks they are holding a magic wand, but actually shoot up a mall, they don't have intent but the gun violence still resulted in death. Would that not be a mass shooting in your intent-based definition?
Your explaining the difference but not explaining why it makes a difference.
To matters of gun regulation, of safety in public spaces, of trauma to the affected, of national reputation (pick any one, or all, or something else) why does the intent change anything?
I'll start off: To have the intention to mass-murder purely for the sake of mass murder could be worth isolating and studying because that is a specific and extreme psychological problem worth solving. However, not all mass killings (with intent, for your sake) will have that psychological trigger at root. A religious or racial extremist, for example, is different than a disaffected teenager.
In this circumstance, intent is interesting if one is interested in those other things (psychological issues in American youth, the spread of religious and racial extremism), but ultimately are secondary issues when it comes to measuring gun violence. A mass stabbing by a racial extremist, or a teenager blowing up their high school with fertilizer would still need to be measured.
You are complaining about this organization's yardstick, but I don't hear a compelling alternative from you for this specific measure. You are saying they should be measuring a totally different thing, which is arguably irrelevant to this measure.