@Tersione The demon sort of 'commanded' the child to wish for one more thing: for the child to wish he can become the demon's child. It's a non-contract wish, though, since the kid already gave up his soul by using his previous wish (the hug).
@amir1373 It's not that the demon will give the kid one more wish in exchange for "adoption", when the kid used up his previous wish (the hug) he already became a demon, so now the big demon himself wants to take care of the kid out of kindness, ironically (he's a demon : O).
I think a clearer TL like this would've been less misleading:
Demon: I will allow you one more wish...
Demon: You may become my child.
The idea is that the demon wants something, but is too prideful so he says it in a way that's like 'it's not like I want you to be my child, I'm allowing you to be my child'.