EVE uses an open economy based around supply and demand.
The effects are a bit less predictable, but the general idea is outlined in this thread.
The idea of Burn Jita is to kill everyone and everything in what is currently the largest trading hub in the game, Jita. By doing this, killing everyone bringing in supply, shortages will be created, driving up demand and therefore the price. By destroying the their ships, they'll also be costing them currency to replace them and the cost of the cargo lost and inflating the cost of building ships to some degree. However, because of insurance, the victims will actually be getting a flood of money back.
It won't "destroy" the economy. It will shuffle it a bit. Jita will become a less hospitable place for trade for a while and traders will go elsewhere. Resources will be a bit more scarce. By forcing trade to go elsewhere, the wealth should become slightly more distributed. Depending how concentrated the market in EVE is, the amount of wealth distributed could be a lot or not very much.
The reason the developers support this is because it is part of their design philosophy to let the game play out as the players interact with it and to interfere as little as possible - it even says so in the article. The developers might look at it as acceptable/good because it's all good fun and it won't really "destroy" anything - it is a game after all.