Do stepchildren have any legal claim to anything when a stepparent dies?
They were never adopted and the stepparent had a child of his own.
Unfortunately, for purposes of inheritance--i.e. for purposes of intestate succession, which is how a decedent's (deceased person's) estate is distributed in the absence of a will--step child is not a recognized relationship. That is, if there is no will, the step child does not inherit anything (and therefore, his or her child also has no right to inherit). Only biological children, other blood relatives (e.g. siblings, parents), and spouses have rights to inherit in the absence of a will.
If there is a will, then it's a totally different story. A person can, by will, designate anyone to inherit--i.e. with a will, you can leave the assets to anyone. If there is a will, the assets go to whomever the will indicates.