I think he planned to kill all of them - he went into the room to look for the surviving sister.
Now, not trying to judge anyone. Perhaps in some situations, there is no win/win scenario.
JMO - he was symbolically punishing all of his family. IMHO, it had nothing to do with the inheritance. JMO, he entered adolescence, which is the second phase of separation-individuation, and it starts typically for everyone. It's normal to question and doubt your parents, to stretch the umbilical cord to the maximum, and to rebel. Healthy resolution is always a challenge. But this is where the role of the social group one can trust is so high, and he probably didn't feel he had anyone.
His act is too extreme. It is quite possible that he could have done the same even if he attended a huge public school. Or he could have become suicidal, or self-destructive. But, the studies of the effects of loneliness and social isolation on the level of violence, aggression and disinhibition of aggressive thoughts have been on the rise Post-Covid. Here is one
Both social exclusion and loneliness are aversive experiences that can lead to hostile behavioral reactions, including aggressive behavior. This study aimed to assess whether a social exclusion scenario in the subject’s imagination elicits ...
pmc.ncbi.nlm.nih.gov
Some factors such as narcissism or rejection sensitivity are contributors.
This is the opposite study, and maybe it is the scenario that the parents wanted to avoid.
Social Isolation, Loneliness, and Violence Exposure in Urban Adults - PMC (Urban youths who have been exposed to violence are isolating and it leads to overeating, drinking and physically damaging behaviors).
So Edmonds is more urban and Fall City has a higher index of safety. JMO: the parents probably were creating the best scenario they could think of: rural life on the lake, quiet, safe, the parents dedicate their lives to kids and protect them from unsafe situations, less Internet exposure, homemade food, what could go wrong? Maybe it is that increased loneliness in the most vulnerable one that caused the recoil?
Sad that it seemingly never occurred to the perpetrator that his younger siblings could be silently going through the same process. Nor did he leave them the chance to grow to the age when one starts questioning the parents. But either he viewed his family as a monolith, or the kids were yet at a different phase of development and identified more with the parents, or maybe this is where we enter the area of psychotic, grandiose thinking.