I presume that you're referring to the portions that appear to be handwritten next to the Chinese characters. I'm pretty sure that it's Mongolian. 華夷譯語 was a Chinese-Mongolian dictionary prepared (or at least completed) under the Qing (Manchu) Dynasty.
Good question. The title is "Chinese-Barbarian Dictionary". Apparently it was first started under the Ming. Contrary to what I said earlier, different portions of it appear to be in different languages, including some in Persian and maybe Arabic as well. Jurchen too? This portion does not really look like Mongolian, but I don't know what Jurchen script looks like. It wouldn't surprise me if it was.
In any case, it doesn't include any Burmese, at least not in the section on the Internet Archive. I'd be interested to know what your interest is, Klend.
Huayi Yiyu 華夷譯語 is not a single book, but a generic name given to the glossaries used by the translation departments of the Ming and Qing dynasties. (It includes Persian, known as Huihuiyu 回回語, but there's no Arabic counterpart.)
The glossary in question seems to be Burmese, if we look at the names of the days (Chinese translations followed by transliterations of the names, from page 45-6 of the book, my highlighting):
Yes, this is exactly Burmese Language. I can comprehend many Burmese words in this book, even though it was written in old Burmese script. I think it included at least 3 scripts or languages. one is old Burmese. It was written top to bottom like Chinese in this book. Normally, Burmese characters is written from left to right.
Hua Yi Yi Yu 2 is Burmese and 3 seem to Tai Yuan (Lanna). These two used similar scripts.