In the old days before air conditioning they used wind catchers to get air to flow from the cooler parts of the building using the ever present winds being caught in the towers. This was a common Middle Eastern construction. See more here.
There are not very many old buildings left in Kuwait. Everything since the first Gulf War has pretty well been demolished to make way for the new.
You can also see a very interesting post on this and other old buildings in Kuwait here: http://intlxpatr.wordpress.com/2009/01/06/blue-skies-old-ruins/#comments The comments are very interesting.