in at least one of the cases

Ah, but the majority of them were not. His status as a Minecraft player offers minor motive in less than half of the events, making it only part of the equation.

However, the article says in big letters, in a prominent position of the HEADLINE that he was a Minecraft player. This suggests heavily that his being a Minecraft player was a major factor.

My criticism is about taking an aspect of a person that minimally impacted (1/3 of the cases, that's a minimal, albeit significant, amount) the story and placing it front and center for attention. Consider how these minor edits all read very differently:

• 13-year-old Minecraft player confesses to swatting, police say.
• 13-year-old gamer confesses to swatting, police say.
• 13-year-old student confesses to swatting, police say.
• 13-year-old boy confesses to swatting, police say.
• Juvenile confesses to swatting, police say.

Consider what the take-away is for each one.

1. Implies that Minecraft is a major factor, when in fact it is simply a hobby related to one of the cases. Hence my allusion to trombonists and stamp collectors.
2. Implies that playing games is a major factor, which suggests to people influenced by headlines (more than you think) that playing games influences people to call SWAT teams on other players. Which happens, but has more to do with anonymity, the Internet, and lack of consequences (like with this instance) than anything.
3. Implies that his being a student was a major factor. This one has more merit because TWO of the three cases were against people he met in school; a fellow student one, a teacher another. But this makes for a different headline, one that doesn't immediately apply to a technology website like arstechnica.
4. Implies...very little, actually. It's a no-nonsense, fact-based assessment. Which is exactly why it wouldn't get put on arstechnica, because it has nothing to do with that website. This is the heart of the matter; the writer chose the headline specifically to give the post a reason to exist and to draw attention. One part business, one part sensationalism.
5. What happens when we remove the age? Our image of the boy transforms from a young child who barely understands the consequences of not feeding a goldfish into the image of a rebellious teenager whose anger has no clear outlet, so he does whatever he can to release it. This is probably closer to the truth than any of them.