Simple math will tell you that this increase cannot be due to desalination. Look:

Volume of the Persian Gulf = Area (251,000 sq km) * average depth (50 m) = 12,000 cubic km approx.

Total amount of desalinated water produced in the world, per annum = 86 million cu. m = 0.086 cu. km,

So if all of the world's desalinated water was taken from the Persian Gulf, for 150 years, the salinity would only increase by 0.08*150/12000 = 0.1%, roughly.

Edit: the entire article is bad, and the headline is sensationalist bullsh#t.