No. For tax purposes, the kinship created by simple adoption is not considered for the calculation of gift or inheritance taxes (Article 786 of the General Tax Code), except for certain exceptions. However, these exceptions apply only to the adopted person and not to the adoptive parent.
Your stepfather will not be eligible for an allowance and will be taxed on the full amount you give him at a rate of 60% (Article 777, IV of the General Tax Code).