Are reasoning traces required for distillation? Well they are if what you are trying to distill is reasoning, such as coding expertise.
Do you need reasoning traces for "LLM as judge"? No, but it would be highly perverse to call that distillation when there is a more accurate name for it - LLM as judge.
If you want to call use of Anthropic's redacted model outputs in any fashion that violates their terms of service (using them them to help develop anything that competes with Anthropic) as "distillation" then I can't stop you, but it reduces their claims to a joke.
Finally, as noted, OpenAI (who are just as anti-Chinese as Anthropic) said that Kimi 3 can't be explained via distillation (even true distillation!!), or even "anything like it". But random internet guy, you, disagrees. OK.