Answer: No. He is not ambidextrous.
Step-by-step explanation:
Being ambidextrous means that the kid should be able to use both of his hands and that there should not be a preference for one at the expense of the other one. In this case, the kid should not view a particular hand as the stronger hand.
With regards to the question, we are informed that the kid has the ability to write with his left hand but not his right but that he's able to use his right for other tasks because that's his strong hand. This shows that he is not ambidextrous as he can not write with his right hand. It shows the hands aren't being used equally.