Your immune system kills them. However your immune system needs time. Your body has to randomly produce antibodies in response to the virus. Once one antibody is able to attach to a virus immune cells can then destroy the virus and the antibody that attaches is now ramped up by the immune system. If your immune system can do that faster than the virus can cause damage you have a mild course. If not you can die.
The 2 medications mentioned seem to interfere with various parts of the virus lifecycle and/or our inflammatory response that leads down the path to ARDS(acute respiratory distress syndrome). With diminished replication and your inflammatory response under control your immune system has time to destroy and clear the virus from your system.
There is a nice review of the immune system cira 2000 in the NEJM.
The Immune System - Part 1
The Immune System - Part 2
Sorry that it requires a subscription.
Thanks.