The term "stepfather" is generally used to refer to the husband or partner of one's biological or adoptive mother, with whom they have no blood relation. So, if your mother is getting re-married, her new husband would indeed be considered your stepfather.
However, the legal implications and rights that come with the title of stepfather can vary depending on the jurisdiction and the specific circumstances of the marriage. For example, in some places, step-parents may be granted certain rights and responsibilities, such as being involved in the child's life or having a say in important decisions. In other cases, step-parents might not have any legal rights over the children unless they adopt them.
Since you mentioned that your mom has no legal right to see you and your siblings, it's important to understand the laws in your country or state regarding step-parents' rights and their involvement with children in blended families. Custody and visitation rights can be complex legal matters, and you may want to consult with a family lawyer or seek legal advice to understand your specific situation better.
Remember that regardless of legal rights, family dynamics and relationships can be sensitive and emotionally charged. Open communication and understanding among family members can play a significant role in navigating these changes and building positive relationships within the family unit.