The problem is really a semantic one, I'd say. The issue is what is defined as "a virus". Typically a virion is used as the canonical representation of a virus,

The problem is really a semantic one, I'd say. The issue is what is defined as "a virus". Typically a virion is used as the canonical representation of a virus, but this is no more accurate than calling an egg a chicken. This is merely an infectious particle, one part of the viral lifecycle. Properly, the virus when it is operating after infecting a host is just as much "the virus", and in that phase is very much easier to see as alive.