That's not the strict definition. You are using an extremely loose definition. You are missing two key aspects. First, this defintion of species only applies to sexual organisms, and it's about sexual reproduction. Not just any kind of reproduction. Second, the offspring of said sexual reproduction itself must be fertile. So no, in no way can you ever say viruses are human with this definition.
Viruses clearly reproduce with humans. By a strict "reproduction / species" definition, Viruses are human.