I mean it sounds plausible but I'm not sure anyone really knows. What I have found out though is that the numbers one through 5, including 'muoy', are the same or very similar in the Mon language as well as Vietnamese. In the case of Vietnamese, they may have incorporated those particular numbers from Khmer or other Austroasiatic languages like Chrau, where 'muoy' is also used.
https://omniglot.com/language/numbers/chrau.htm
I still think it is very plausible that 'Muay' is derrived from the Khmer word 'Muoy'. The Thai term "Toi Muay' and 'Chok Muay' (the original names of Muay Thai) are made up by two words. We know that the words 'Toi' and 'Chok' are undoubtedly Thai words, meaning 'Fight' or 'Hit'. They say 'Muay' means boxing, and then the name "Toi Muay/Chok Muay" would mean 'to hit each other boxing' or 'to fight boxing'.
Because of the Malay name for S.E.A. fighting of 'Tomoi', we know that the Malay name is undoubtedly copied from the Thai name 'Toi Muay'. Toi Muay --> Tomoi. We know that the people in Southern Thailand were Cambodian-Thai mixed. There is numerous evidence of the many Khmer communities who lived in Southern Thailand from at least the 14th century. They also were in close contact with many of the different Malay peoples in the region. So we know that 'Toi Muay' was the original name for Muay Thai in Southern Thailand. Now, we can conclude that the Thai word 'Muay' now is a Thai noun and verb, meaning 'Boxing/fighting'.
We know that in Khmer language the word 'Muoy' (មួយ) is an adjective, and it is used with nouns from different categories. The name 'Muoy' is the Khmer name for the name of the number 'one". Also, the Khmer term 'Muoy' is a powerful adjective that can be used to make the noun give the supreme status. For example, we know it is still used with the words 'Roam' (meaning dance: រាំ) and with the word 'Pech' (meaning diamond: ពេជ្រ). These Khmer words plus the adjective 'Muoy' are 'Roam Muoy' (រាំមួយ) and 'Pech Muoy' (ពេជ្រមួយ). Interestingly, the Khmer word for diamond 'Pech' (ពេជ្រ) is now written in Thai as 'Petch' (เพชร), while it can also be applied for other stones, in particular gemstones. Only in the Khmer language do we find 'Pech Muoy' (ពេជ្រមួយ) as an additional name for diamond, but with the additional adjective of 'Muoy', which then originally would indicate that 'Muoy' was used as an adjective to signify supreme status; in this case the supreme status of a gemstone in Khmer language --> Pech Muoy --> number one gemstone-->diamond. In 'Pech Muoy', the Khmer adjective 'Muoy' refers to the supreme status of the diamond. In 'Roam Muoy' the Khmer adjective 'Muoy' seems to indicate 'the nr.1 dance'. So, from these Khmer examples we can conclude that the Khmer term for the number 1; 'Muoy', is used in Khmer as an adjective which in Khmer language makes a noun give supreme status. Both these Khmer meanings can be applied to 'Toi Muay/Chok Muay'.
An example of 'Roam Muay' can be found in this video:
Roam Muay. The word 'Roam Muoy' seems very interesting, because there exist a very similar word in Thai which is strongly associated with Muay Thai; it is the term "Ram Muay". The word 'Ram' in Thai means 'dance/to dance', and if you compare both symbols of the words, you can see that both the Thai and Khmer symbols are related in this case, and undoubtedly are both derrived from the same Khmer origin. You can see for yourself: the Thai symbols are รำ, and the Khmer symbols are រាំ. If you attach the two Thai symbols of the word 'Ram', you get the word 'Roam' in Khmer, which in both languages means 'dance/to dance': รำ --> រាំ. The word 'Ram Muay' doesn't refer to the dance, though, but to the music of Muay Thai. However, the music is used for the fighters to perform the 'Wai Kru'-dance, and it is possible that the word for the dance and the music once became the same word, while Wai Kru became to name only the dance, because of the ceremonial meaning ('Wai Kru' means 'to greet/to pay respect to the Guru').
Because the original Khmer term 'Muoy' could have been lost in Thai language, and only used for the names concerning Muay Thai, it is understandable that it is still found in Khmer language as the adjective 'Muoy', while in Thai language it became the name of 'Boxing'. The Khmer speakers of Southern Thailand all switched to speaking Thai Language. The Southern Thai language has many Khmer terms that are no longer used in Cambodian language, but which are still preserved in Southern Thai language, according to study. It explains how a Khmer term became only used with the specific art of Muay Thai that was originally named with a Khmer term. Since the original Khmer term 'Muoy' had a much more broad appliance, it is therefore also logical that it is still used in Khmer langauge today, of which I have found the two names of 'Roam Muoy' and 'Pech Muoy', of which 'Roam Muoy' was originally the same term of the Thai word 'Ram Muay' which are andoubtedly related words which both became to mean different terms in both languages.
Does this prove 'Muay' in the name 'Muay Thai' is derrived from the Khmer word 'Muoy"? No, it is possible that 'Muay' was originally a verb and a noun, and not just an adjective, which it solely is in Khmer. The Thai word 'Ram' can be used as a verb and a noun. For example; the word can be translated as 'Thai dance' to 'Ram Thai' (รำไทย), but also as 'traditional dance' as 'Fon Ram' (ฟ้อนรำ). This can also be applied to 'Muay' as in 'Chok Muay' and 'Muay Thai'.
However, where it becames interesting, is the fact that there seems to not exist any word for 'Muay' in any of the languages that are related to Thai language (for so far as I have been able to research), and which are part of the Tai-Kradai language family. The word 'Muay' only exists in relation to fighting within the communities that practice Muay Thai. So we have proof of a related word in Khmer, which is 'Muoy' (មួយ: number one), but can we find any related word in any of the Thai related languages of the Tai-Kradai family? Ethnologue lists 95 languages in the family, with 62 of these being in the Tai branch. If we find the word 'Muay' only in the languages of Thailand and Laos, both of who's culture have been greatly influenced by ancint Khmer culture, then shouldn't we find a related term to 'muay' in any of the other 93 Tai languages? And if not, would this be a great indication that 'Muay' is indeed' derrived from the Khmer word 'Muoy'?
You said the following: "
The word "Muay" in the thai-Lao language has two different meanings. The first one which meant "Fighter or Combat" the second meaning can also refer to the word "Style". I saw Thai folks use the word muay to refer to "style"."
Can you provide me with the word for Thai and Lao 'style' you mentioned? I don't know which word you mean, and I would like to find out related words to 'Muay' in other Tai-Kradai languages. I haven't been able to find any so far, so I don't know which word you mean. I want to investigate the use of the word 'Muay' in languages related to Thai language.
Thanks for providing me with the Chrau numbers. It does seem that the word 'Muoy' is a widely used Austro-Asiatic name for the number 'one'. It would be interesting to know if related words to the Khmer word 'Muoy' are also used as an adjective, like in the Khmer words 'Roam Muoy' and 'Pech Muoy'.