Grammar in Indonesian language is normal: biarkan bermain anak anak itu. Learned it in school. I found a lot of that kind of wrong sentences
It wont be too wrong if "mereka" and a comma is added, it just add emphasis on the action "play" rather than the childrens.
"biarkan mereka bermain, anak-anak itu."
"let them play, those childrens."
I think 'Mari anak-anak itu bermain' should also be valid?
"Mari" is like a polite form of "let us", "let's go" or "come on" to the person listening. Whereas this sentence the speaker's not speaking to the childrens.
You could however say "Mari biarkian anak-anak itu bermain" which would mean "Let us let those childrens play"