The word damage" can mean various things, but in this case I have to agree that using old gas in your stove can do some harm. What happens is this: The chemical makeup of white gaswhich is basically the stuff you put in your car, minus certain additiveschanges as it ages. In time it becomes a sort of varnish-like substance. It still burns, but can leave behind deposits that can clog up the burner in your stove. If that happens, the damage is reparable, but you might find yourself stove-less halfway through a trip.
Old gasoline or white gas is difficult to get rid of. You cant pour it down the drain or sewer, as treatment plants arent designed to handle it, and you dont want it ending up in lakes or streams. I would also never suggest that you dig a small hole in the ground, pour the gas into the hole, and follow it by a lit match, because that is of course very dangerous.
The best solution is to mix it with fresh white gas at a ratio of 4:1, then use it up. If you do need to store opened fuel for more than six months, add a fuel stabilizer such as STA-BIL, which slows the cracking" process that turns gas to varnish.