The UAE as a whole is not in serious economic problems. Dubai, one of the constituent Emirates, is in a bit of a financial hole, but will probably be bailed out by their oil rich neighbours.
Not sure what Saudi Arabia has to do with it all, as it's different country.
You can watch a lengthy video clip of Meydan here, scroll down to Meydan Marvel. The place is quite impressive.
While it does have the largest grandstand in the world, 1.6km (1 mile) long, the article and thread title are misleading in that it is not the biggest racecourse in the world, there are a number of racecourses around the world that are larger in size (i.e total area covered).