No one, least of all the zoos themselves, claim to be the ideal solution to the problem of disappearing species. From a conservation standpoint, zoos (the good ones, not the ones with lots of tiny concrete cages) serve as a stopgap. A stopgap may not be ideal, but it may prevent a species from being destroyed before an ideal solution can be found.
What purposes do zoos serve beyond entertainment?
Research - Most of the real work zoos do takes place behind the scenes. Zoos (especially natural habitat zoos, such as the San Diego Wild Animal Park) provide an environment where animal health, behavior, etc. can easily be studied. This knowledge may be crucial for reintroducing the animals into the wild in the future. This research may not be possible, or may be less effective, in the animal's original habitat for political or logistical reasons.
Funding - I admit, I'm guessing on this one. I don't actually know if the public side of zoos does much to fund the behind-the-scenes work. However, I would guess that it does, both directly (through ticket costs, concession stands, etc.) and indirectly (through donations). The money for the ideal solution doesn't just magically appear, and zoos are a good way of getting people to pay attention to the cause.
Species preservation - Zoos provide both a safe place for animals to live when their habitat is threatened, and a place where their breeding can be controlled and optimized. This is especially important for extremely endangered species - there may be enough individuals left for the species to survive, but not without human intervention to optimize genetic diversity (not to mention protecting the remaining individuals from poachers and other threats).
Just for the record, many zoos are dedicated to preserving plant species as well as animals.
Will zoos protect every species on the planet from extinction? No, obviously not. Their resources and knowledge are limited. Does that mean that their efforts should be stopped because they can't help everyone right now? (Why don't we stop cancer research as well? It's obviously pointless, since we don't have a solution for everything right now, and people are still dying of cancer while this research is going on...)
Education - Zoos will not magically make every visitor become a rabid environmentalist. However, zoos get millions of visitors a year. If they manage to convince even 1% of their visitors to do something to help the cause (through donations, their choice of job, or a choice to recycle or not buy poached ivory), that's a huge number of people who might otherwise have not become involved.
Could this be done through videos and other media? Perhaps to some extent, but the impact of standing 10 feet away from an elephant and seeing one on tv is different. And you're still presumably confining some animals somewhere because they don't have anywhere else to live - they just wouldn't be on public display.
As for the zoos with tiny concrete and wire cages which exist soley for entertainment purposes, I don't believe they serve any real purpose, even from an educational standpoint (they obviously didn't do anything to educate the author of this article on what kind of good zoos can do). I think the zoo effort should focus on areas where the most good can be done. And really, I'm not convinced of the morality of public display of animals. However, I do think that modern zoos on the whole do more good than harm.