This refers not to a young child but to a youth who was a continual drunkard and was persistently rebellious, stubborn, gluttonous, and disobedient (which describes many contemporary teenagers). If a son consistently refused to abide by his parents’ authority, the men of the city were to enforce swift capital punishment.
However, there is no record in Scripture of even one rebellious youth in Israel being put to death by stoning. The Law of Moses was read to all of Israel, so no doubt all children were made aware of this law’s terrifying threat before they reached their teenage years. (That it was an effective deterrent shows God’s wisdom in setting such a harsh penalty.) In contrast, each year in the U.S. thousands of youths die through drunk driving, violence, alcohol poisoning, drug abuse, etc., as a tragic result of their rebellious lifestyles.
That same merciless Law of Moses will judge all of humanity on the Day of Judgment. However, Jesus took our capital punishment upon Himself so that we could leave the courtroom without suffering the consequences of our sins. All that God requires of us is that we repent of our stubborn, rebellious, and disobedient lifestyle and trust in the Savior before the great stone of God’s Law falls on us and grinds us “to powder” (see Luke 20:18).