My question here is: why is this so rare? Given how many spermatozoids are involved in every sexual contact, why doesn't it happen much more often for two of them to fertilize one egg?
A polyploid zygote is completely nonviable, a pure waste of the egg, sperm, and other mating effort that went into it. It's in the interest of the mother and the father for the egg to be fertilized by exactly one sperm.
But it's in the interest of an individual sperm to be the one that fertilizes the egg instead of dying uselessly. So they get faster, more efficient, and more penetrant over time. When they're too effective, multiple sperm may get into an egg before the defenses are up. (Which, again, just kills the sperm that "won" the race, so you don't expect to see incredibly rapid progress in this area.)
Oceangoing eggs respond by having a fertilized egg's defenses go up really quickly, because the egg is floating around in the ocean and it's hard for the mother to influence that environment.
Female mammals have responded with slower defenses, but internal characteristics that tend to retard or hurt sperm as they make their way towards the egg, meaning that it's rare for multiple sperm to all get there at once. This is good for avoiding polyploidy, but bad for fertility -- it is not necessarily the case that even one sperm will make it.
It's interesting to see competition among sperm hurting the reproductive chances of the male and female producing and accepting it.
My understanding (I'm a doctor but NOT an expert in this area) is that it usually is a long, difficult journey to the egg, and the chance of many getting there at exactly the same time is low. When a spermatozoan buries into the egg a reaction is caused which prevents other sperm from being able to penetrate.
An expert may be able to clarify, but I think this is the gist of it.
Given that this appears likely to cause the death of one or both twins (on the assumption, not true here, that there's no such thing as prophylactic surgery to remove precancerous gonads), it doesn't seem like the rarity really requires an explanation. Contra what the article says, these twins are not in good health.
If you're asking "what is the mechanism that makes sure this doesn't happen?", as opposed to "why doesn't this happen more?", that's a better question and I don't know the answer.