If they have any sense, they should be. It would be permitted under the licence, too (unless I'm misreading the k3 licence).

Anthropic has more than $20 million in revenue so as per the k3 license they would need to enter a special commercial deal if they wanted to use it:

https://huggingface.co/moonshotai/Kimi-K3/blob/main/LICENSE

No, keep reading:

> The requirements set forth in Sections 2 and 3 do not apply to: (a) internal use of the Software, defined as any use that does not make the Software, its outputs, or its underlying capabilities available to third parties; or (b) any use of the Software accessed through Moonshot AI's official products or certified inference partners.

"distilling" from their own hardware would be an internal use of the software.

In my personal opinion, distilling its output into training another model that is then provided to users does fall into the category of "making its output or its underlying capabilities available to third parties", but I could see the argument that it doesn't.