Both good answers (above), but there’s more.
All life started in the water. The cellular organism, being a single cell, was always in direct contact with the surrounding water, and drew the raw materials it need directly from that life giving fluid. As multicellular organisms evolved, they had to develop ways to get those nutrients to “interior” cells–cells that were no longer in direct contact with seawater. Thus the circulatory system, which circulates blood–essentially, seawater synthesized by the organism. “We” left the water millions of years ago, so our bodies had to develop closed systems, cut off from the seawater. We carry our closed system of seawater around with us.
Fish never left the water, so they never needed to evolve such a physically isolated circulatory system. Mostly through their gill membranes, fish still maintain a very close osmotic relationship with the water they live in. If the water chemistry changes, a fish’s blood chemistry will change too, in order to maintain an osmotic balance with the water it lives in.
This means, of course, that fish are even more sensitive to the chemicals that surround them than we are. Along comes evolution and finds a way to take advantage of this to manage fish population density.
As a fish population grows, naturally the concentration of the fishes’ metabolic byproducts–i.e., bodily waste–increases in the surrounding water. As these chemicals (Ammonia => nitrates => nitrites) become more concentrated in the water–and therefore, remembering the osmotic gill membranes–in a fish’s blood–the fish’s metabolism is affected. In response to these signals of overpopulation, a fish’s growth may slow, or stop entirely. And to vastly oversimplify, the fish begins to die. A change in water chemistry can return things to normal, but for all intents and purposes the fish is now on the downslope of its life cycle as opposed to the upside.
In a bowl, without adequate water changes to diliute the waste chemicals, a fish’s growth will be stunted, and it won’t live a normal life span. People may triumphantly claim that their goldfish lived 5 or 6 years in a bowl, but a goldfish in its native environment–cold, clean freshwater–it may live as long as 40 years. So 5 or 6 years is more like infanticide than success.
So it’s not so much the physical limitations of the bowl. It’s the chemical issues. I’ve had goldfish live well in bowls if I feed them no more than frequently than every second or third day, and change the water frequently. (I’ve never had a goldfish for 40 years, but I’ve given a few away after keeping them healthy for 4 or 5.)
And the article says “round bowls caused fish to go blind.” This makes some kind of sense if you realize that fish eyes protrude somewhat from their head, and a goldfish may spend a lot of time sliding along the inner surface of the bowl. This is less likely to happen in a container that isn’t globular, for obvious geometrical reasons.
I’ve always tried to talk people out of putting goldfish in bowls, but I’m not sure I’d go so far as to criminalize it.