Do step children have any rights as next of kin?

Only step-children who were legally adopted by the decedent would be considered legal next-of-kin.

There is a rare exception in states such as New Jersey in which the estate of a person who dies with no other heirs at law can pass to step-children. These issues are governed by state laws of intestacy.

You can check the laws of intestacy in your state at the related question link.