"How did they classify Rittenhouse's self defense killings?"
They probably didn't.
But since you brought it up, here's ADL's take on the Rittenhouse verdict. You may find yourself among those here who agree with 100% of this: www.adl.org
As soon as the jury announced its verdict, online extremist spaces erupted in cheers and self-congratulatory rhetoric. Supporters heralded the Rittenhouse verdict as a victory for the principle of self-defense and providing legal precedent for violent responses to perceived threats, and some argued that people no longer need to avoid acting during tense situations for fear of legal repercussions, a potentially dangerous development.
After one user on Patriots.win wrote, "Antifags and BLMKKK gotta be --------. We have permission to defend ourselves now," [sic] another responded, "We don't need ------- permission and never did. But now, it's a legal precedent."
One boogalooer on Twitter wrote: "WE CAN PROTECT OUR COMMUNITIES NOW REFERENCING RITTENHOUSE V. Wisconsin."
On Telegram, QAnon John wrote, "This case is a MAJOR turning point in the quest for JUSTICE in our country. Especially in terms of the 2nd Amendment, and self-defense cases moving forward ... The precedent set in this trial will be one that is revisited, and referenced for the unseeable future."
Also on Telegram, Aaron Chapman, the leader of the neo-Nazi group the Occidental Templars, praised the verdict as giving "good Americans legal precedent and license to kill violent commies without worrying about doing life in prison if we defend ourselves in a riot. This will also show militia types that they don't have to avoid the riots to protect themselves legally."
One user in the Proud Boys public chatroom on Telegram shared an image of the snake from the Gadsden flag biting the fist from the antifa logo with the caption "YOU WERE WARNED." Beneath it, the user wrote, "#Kyle #FAFO" ("FAFO" stands for "---- around and find out.")