My father's half sister just posted her AncestryDNA results.
I did not come up as a match, nor did my sister.
Does this mean that my father's dad is not really his dad, or could there be another explanation?
It absolutely means that your half aunt is not biologically your half aunt or another close relative.
There are 4 possibilities:
(I'm assuming from your question that you already know that your dad and his half sister have different mothers and are assumed to have the same father.)
If your father's "half sister" is expected to share a father with him then one alternative may be that your father has his expected father but his "half sister" does not.
From your description, your paternal grandfather had two wives. One is the mother of your father and the other is the mother of your aunt. @cyn's point
- Your aunt's dad is not her biological dad
is the most likely scenario. I would look for a previous marriage for your aunt's mother or a birth record for your aunt in her mother's previous married name, or her mother's maiden name.