Not a serial killer

Well considering it's fiction I don't really think anyone cares. He doesn't have to have a certain type of psychology in order to be a serial killer or mass murderer. Those classifications, by police at least, are made by sheer number of murders committed and in how much time. Besides, statistics show that most serial killers are legally pronounced completely sane.

Not sure where you received your education on this topic, if it was a university I would ask for your tuition back, but it sounds more like you're an expert from watching too many episodes of law and order.
Within the time frame of the movie it would be hard to categorize him as either as he only murdered two and a half people, I say a half because his final killing was of a bad guy that did try and kill him but is kinda open to interpretation because of the exact timing of the situation.
Now through other information in the movie I can say he is absolutely a serial killer and not a mass murderer. First and foremost mass murderers do not collect individual "trinkets" from their victims, this is a well know trait of many serial killers. A serial killer kills out of an internal need for it, which they very often rationalize for themselves, I.e. Doing gods work. Once they kill enough there is then a cooling down period where the need to kill is quenched and they return to everyday life until the urge builds up again until they must kill to satisfy it, this cooling down period between killings could be weeks or years. Mass murderers typically are one event killers that very often ends in their own death either by their own hands or police.
What you have in this movie is a serial killer who is forced into awakening his inner killer, now because he has his ritual he cannot just kill someone and not take his prize, so he begins doing what he knows and satisfies his craving once the monster inside has awoke.

Generally serial killers have a deep psychopathy generally associated with childhood trauma, where mass murderers tend to have minor mental problems and snap or loose control. Both typically lack morals, empathy, regret. However neither are typically declared insane as at the time they absolutely know the difference from right and wrong and do understand their actions at the time are very wrong, big difference between legally insane and clinically.

"We are all born ignorant, but one must work hard to remain stupid." - Benjamin Franklin

I think you are a bit confused. A mass murderer would be someone that killed multiple people at one time, a serial killer would be someone that also killed multiple people but did it over time. Considering Henry's character was taking trophies and sticking them in a safety deposit box I think he would clearly fit the definition of a serial killer.

Whatever, I'd give him my turn, too.