That is a pretty awesome demo.
So there is more than "water rusting" going on here.
Chemically, the gasses in the exhaust dissolve in the moisture present forming various acids that corrode the unprotected metal.
Exhaust gas is a mixture of water vapor (H2O), Carbon Dioxide (CO2), Sulfur Dioxide (SO2), and Carbon Monoxide (CO).
CO2 dissolves in water (H20) to form carbonic acid (H2C03) and SO2 dissolves in water to form Sulfurous Acid (H2SO3), and Carbon Monoxide dissolves in water to form Hyposulfurous Acid (H2SO2).
Once formed in the exhaust, if the tailpipe does not get hot enough to drive off the water, the acidic liquid lays in the pipe and does its corrosive work.
If you heat the pipe all the way to the end, by driving at least an hour or better, it will evaporate the water and break down the acid into non corrosive gas which is ejected.
The worst thing you can do with a combustion engine is to run the engine for 20 minutes and shut it off. Just watch the water pour out of the exhaust pipe on a winter morning when you are warming it up before going to work. That water is very acidic and if you change your mind about going and shut it off, you better hope you have a stainless steel exhaust system all the way to the end!
That pipe in the picture rotted from the inside out; not the outside in ...