Bettas can live in small tanks without filtration and without aeration. However, without filtration their water MUST be changed regularly--not topped off as it evaporates, as evaporation doesn't remove fish waste or nitrates from the existing water. With a one gallon container (the approximate size of this bowl), owners can expect to replace the water once or twice a week, which is no big deal with a tabletop bowl but probably a bit inconvenient with a wall-mounted bowl.
Goldfish, on the other hand, need large amounts of water with filtration and aeration. First, they are large fish--they grow up to a foot in length--and thus need a larger quantity of water to maintain them. Second, they are inefficient eaters and produce a lot of waste, and so filtration (and enough water to accomodate their waste) is a must. Third, they are cold water fish, and cold water holds more oxygen; no room-temperature bowl can provide enough. A single gallon will not keep a goldfish alive long, and will not keep it healthy.
As for other "easy-to-maintain" fish, I have my doubts. A fish may be hardy enough to survive a while in a tiny unfiltered tank, but hardy and healthy are not the same things. In addition, most of these fish will need at least one gallon PER fish, which puts schooling species at a distinct disadvantage.
Which brings me to the reviewer who keeps a betta and two African Dwarf Frogs in this bowl and only changes water once every two weeks. Despite the fish lasting 'a whole year' so far, the tank really is overcrowded and under-maintained. The proof is not that the fish and frogs have lasted a year, but whether they last their full lifespan--seven years for the betta, between ten and twenty years for the frogs.
