Well stated.
Is it possible his islamism was a factor? Sure! That entire belief system increases a person's propensity for murder. The divorce could very well be because he didn't approve of his daughter's "western ways".
But because he killed everyone, including his son (I'm assuming Ali is a boy's name) and himself makes me suspect that it was a wish to wipe out the entire family and put himself out of his misery rather than carry out a religious obligation.
According to other interviews and articles, the son Ali would side with the sister. Dad would take away her phone and either the mother or Ali would give it back to her. The son was disobeying the father so he was killed, too. There was no greater statement he could make against the western Christian world than to dress up as Saint Nick and murder them all on Christmas Day.