It's a virus that "lives" off another species of virus.
I know what a parasite is, but it seems to me that a “parasitic parasite” is redundant.
So the parasite is parasitic to a parasite.
Given that viruses can’t do anything without having invaded a full fledged cell, then it sounds like the phage gets cells to eliminate the other virus, rather than attacking the other virus in the wild.
This might be an interesting concept for the field of medicine. Imagine an anti-flu virus which would be benign to the human body but set a significant number of its cells up to pro-actively attack flu viruses. Or if it’s deemed too dangerous to try on people, then something like this on a veterinary level.
It’s a virusitic virus!