Is it permissible to allocate a portion of zakat al-mal to one's young, orphaned nephews for their training expenses (such as basketball), knowing that they have sources of income and funds for the future?

It is not permissible to use zakat to buy toys for orphans. Zakat is for the poor person who does not find what suffices his basic needs of food, clothing, shelter, and medicine. Orphanhood alone is not a justification for receiving zakat; an orphan is only given from it if he is poor. An orphan who has what suffices him is not eligible for zakat.