It always helps to define your terms.

The link below is to an interesting  on how to portray and analyze.  It is a good step in a useful direction.  A common vocabulary would facilitate communication and threat estimates among states, between organizations, and within them. It would facilitate the academic research, too. To deal with a problem, first you have to identify it, and then you need to be able to talk about it.  If you can't do the second, you probably still have some problems with the first.

That said, I don't find this iteration to be perfect.  What is?  Focusing on "violent extremism" rather than "terrorism" is a good idea.  "Terrorism" has too much baggage.  I'm not sure we could find a consensus on what constitutes "extremism," though.  Can it include actions by official representatives of states?  Must the target be innocent, or civilian (the two are not the same)?  Can a drone strike, or an attack by Special Forces, be characterized as "violent extremism"?  Violent, definitely.  But some of them SF guys seem pretty extreme, too.

Not assuming the religious angle is probably a good idea.  But does it have to be political?  If so, how political?  I don't include an act of a Lone Wolf that has no more connection than an after-the-fact claim of responsibility to be the same as someone who is inspired--Phil Walter's got that right.  But should we include the loser who aims to be playing suicide-by-cop the same as someone who thinks (whether he's right or wrong) that his act will contribute to a desired political outcome?  It seems that some serial killers could be violent extremists, but certainly not all.  We could include the self-motivated murderers of abortion doctors, but some are "saving babies" while others want to change the law, and most probably hold a mix of motives.

Making a particular religious orientation optional is useful.  People with different orientations (or none at all) may well behave differently.  Typing could be useful for profiling, and making comparisons.  But should politics be optional?  I don't think so.  The "psycho killer" is different in kind, not degree.

Toward a Common Lexicon of Violent Extremism - Lawfare