Adverbs modify the verb. Adverbs ending in -ingly denote the manner in which something is done not how the subject feels while doing something, so double check that this is, in fact, your intention with each of these sentences.
A kid is playing a game interestingly.
This means that the way in which the kid is playing is interesting. It does not mean that the kid is playing the game with great interest.
...the boy said frustratingly/irritatingly
Likewise, the adverbs here imply not that the boy is frustrated or irritated, but that the manner in which he is saying something is irritating or frustrating (presumably to his parents as they are the people to whom he is speaking).
If you want to describe that the boy is irritat*ed* or frustrat*ed* (as opposed to irritat*ing*- making others feel irritated) you could say frustratedly- though it would not be particularly eloquent to do so. As others have suggested in comments your best bet would be to switch the order of words:
... the boy said, irritated (or frustrated).
Or, you could choose a verb that means to say something in an irritated or frustrated manner (e.g. whined, groaned etc.).