Russia is flying in Syrian airspace at the request of the Syrian government. The United States is flying drones over Syrian airspace, without Syria's approval. If anything, Russia and/or the Syrian military has the right to shoot down the US drone for violating Syrian airspace. We can argue all day about why the United States still has military personnel in Syria, but at the end of the day, the United States is occupying land in eastern Syria and using Syrian airspace without approval of the Syrian government.
Russia is unlikely to go any further than this and the Syrian government will absolutely not doing anything because Assad doesn't want to be dead by Thursday. Regardless, the US isn't the victim here.