It's not specifically oxygen that's linked to life, it's chemical disequilibrium. Oxygen is highly reactive, there are lots of minerals that will bind it up and there aren't any natural geological processes that unbind it again in significant quantities. If you put an oxygen atmosphere on a lifeless planet then pretty soon all of the oxygen will be bound up in other compounds - carbon dioxide, silicon oxides, ferric oxides, and so forth. There has to be some process that's constantly producing oxygen in vast quantities to keep Earth's atmosphere in the state that it's in.

There are other chemicals that could also be taken as signs of life, depending on the conditions on a planet. Methane, for example, also has a short lifespan under Earthlike conditions. You may have seen headlines a little while back about the detection of "life signs" on Venus, in that case it was phosphine gas (PH3) that they thought they'd spotted (turns out it may have been a false alarm). These sorts of gasses can be detected in planetary atmospheres at interstellar distances, especially in the case of something like Earth where it's quite flagrant.

Even if these are sometimes false alarms, in a "Dark Forest" scenario it'd still be worth sending a probe to go and kill whatever planets exhibit signs like that. It's a lot cheaper and quieter than trying to fight an actual civilization. That's why I can't see why we wouldn't have already been wiped out aeons ago in this scenario.