Are you related to Mr. Wizard?I would think it would change the physical properties of the gas by keeping the byproducts from the gas' evaporation in a dissolved or combustible state.
Since gas is pumped from the ground, it must be distilled and purified. While the end product IS very pure, traces of petroleum-related "gunk" will still remain in the product. Since the main constituent of gas is volatile, it will evaporate fairly quickly if given the chance. As this happens, the I would assume the proportion of the gunk in the gas raises since it stays at roughly the same amount in the tank while the amount of gas lessens from evaporation.
When this is burned, it would create more deposits since the actual gas burns quite easily compared to the gunk in the conditions of an engine.
My guess would be that stabil would work by dissolving and forming an azeotrope with the gunk where it can be carried away in the exhaust with much more ease than if the stabil wasn't present.