They could easily live for years with the right water changes, but will hardly be able to exhibit any natural behaviour in that environment, or grow at natural rate and if the bowl if filterless (even if it's not) they will be exposed to varying ammonia frequently - obviously a health hazard and will take its toll over time.
It's not that hard to keep small species of fish in a filterless bowl with plants and even have them thriving and breeding, but it should be obvious to anyone who's been keeping fish for a while that a species of carp that can easily attain over a foot in length (and fast) is an unsuitable selection of fish for a small tank, let alone a bowl.
I fail to see the point of their experiment, how long those two fish last in that bowl is essentially just chance...for the fish' sake I hope they die sooner rather than have to put up with that crappy environment for their potentially 40+ years of life.