How sound is the statement that Al-Khidr (peace be upon him) used to play with the boys, and that his actions were based on revelation?

The authenticity of the narration about the boy playing with other boys does not necessarily mean he had not reached puberty. The mentioned phrase was quoted from Fakhr al-Din al-Razi's tafsir (definition) (exegesis). It is indeed mentioned in Sahih (definition) al-Bukhari and Muslim that the boy was playing with other boys. However, this is not considered a definitive "textual proof" that he had not reached the age of accountability ( تكليف). Young people, even at the beginning of their puberty, may play and amuse themselves, as seen in the story of Yusuf and his brothers. Furthermore, his killing by Al-Khidr due to Al-Khidr's knowledge of his ultimate destiny does not necessarily imply that he was a child. Rather, he could have been an adult disbeliever, and Al-Khidr knew that if he had lived, he would have burdened his parents with tyranny and disbelief.