Don't things eat mosquitos? Do any of those things matter?
The link-bait title is wrong. No one is seriously talking about eliminating all mosquitos. There's discussion of eliminating two (two) of the over 3,500 species of mosquito, specifically those that carry horrible human diseases.
Maybe you should try reading the article, rather than just the title?
edit: http://www.chron.com/life/gardening/article/Dragonflies-Moth...
Their impact as a food source would be negligible.
Before they were introduced by sailing ships, its not like the bug-eating animals did not have enough bugs to eat.
There’s little evidence, though, that mosquitoes form a crucial link in any food chain, or that their niche could not be filled by something else.