If a virus is non-living and therefore can't be killed, how do antiviral medicines kill a virus?

Viruses. The definition of what is alive or not can be quite dicey. If one defines life as the ability to replicate oneself outside a cell, the viruses are not alive. They often do replicate quite well inside of host cells using its genetic code, either dna or rna, to 'brainwash' the cell into making lots of virus, an acquired genetic disease. Antivirals inhibit the viral replication process.