We had a neighbor who rode BMX and Motocross, so his kid and a couple others in the neighborhood had real dirtbikes at very young ages… his kid was three or four! I was amazed that he had the balance – I couldn’t ride a regular bike until I was six. But his dad taught him and he could handle it.
To me the issue isn’t the age, it’s the family member bypassing the parent in giving a gift that is dangerous and requires intensive training and supervision. Had they even mentioned it at all or did they just spring it on you when they gave it to the kid? That is disrespectful and selfish on the gift-giver’s part, and means that they can not be trusted. If that happened with my son, that family member would be completely cut off from seeing my child—at least not without supervision. Even when someone bypassed me on far less significant issues, they’d at least get an earful, and I would not hesitate to refuse the gift if I felt it was completely inappropriate for my child and wouldn’t necessarily offer explanations, either.
Some folks say, “Sometimes it’s easier to ask forgiveness than permission.” There might be a chance, if I knew that the child has really been wanting a dirt bike, and that the gift-giver is experienced and responsible about safety, I might consider allowing the gift-giver to keep the dirt bike at their home and insist that they train the child how to ride safely, and always with full gear on (NO EXCEPTIONS!), and only when I was present to supervise.