Kun Khmer was known by Thai people as Muay Korat. You see read the reference here: http://www.muaythai.it/techniques/muay-korat/

I'll quote here for convenience:

The first patriarch of Muay Korat was Phra Hensamahan, he encrypted the most articulate and coherent form of this style whose origins can be traced back to the ancient traditions of South East Asia. It’s told that the source of his style came from martial techniques developed in ancient Cambodia during the Khmer’s reign: according to our studies the origin of Muay Khorat would be from the mythical Martial Arts of Angkor Wat, seat of the ancient capital of the Khmer Empire; whose culture strongly influenced the inhabitants in the Khorat area.

MuayThai.it claims to be the official IMBA (International Muay Boran World Association), so it's not like it's a website made by Khmer either.

Cambodia has every right to call Muay Korat style "Kun Khmer". We can't just call it Muay Korat, because Muay is not a Khmer word, and Korat region is now inside Thailand.