The thesis is that the more accurate definition of 'terrorism' is in the method, not the motive. When you kill a lot of innocent people in an extremely public and brutal way, doing something that will dominate the media for days and weeks, that IS a form of terrorism, whatever the precise motive.
As the author of that article pointed out in respect of school shootings and other mass murders, it's about the TV ratings, the publicity, the message, being remembered, becoming a household name; whatever the motivation, personal or political, it's an act of terrorism. That's the correct lens to view this kind of act through.
Again, 100% agree Ranger.
The event itself and the consequences of the event are the key elements of the more recent definitions of terrorism.
The underlying motive (religious, political....) may help us to understand, and may possibly aid identification of high risk people in the future. But the underlying motive does not in itself make (or not make) something an act of terrorism.
Sometimes the motive is irrational and not aligned with anything coherent. Sometimes there no stated or apparent motive. Sometimes no one ever claims responsibility. That does not mean it is not a terrorist act.