Who's RNA does the rRT-PCR test for SARS-CoV-2 target?

The official guide for laboratory testing for coronavirus disease in suspected human cases by the WHO explains the procedure for testing a sample. On page two it states that the test

is based on detection for unique sequences of virus RNA by NAAT such as rRT-PCR with confirmation by nucleic acid sequencing when necessary.

As a layman I’m trying to understand how this works and specifically it this test involves the host’s DNA or RNA. I understand that viruses attack and modify the host’s DNA to get the host to make more copies of the virus.

Does the PCR test explained above target DNA/RNA of the host or does it attempt to find intact instances of SARS-CoV-2 RNA itself — before it befalls a host’s cell? It tries to identify the presence of the virus but does it do it on infected human genes or does it do it on the original virus?