Hello,
I went to UAE by air , in Doha airport they asked me about my Position title in the Qatari Visa (residant or Eqama) since there is a specific career list where they allowed to them to enter the UAE without visa from the embassy (they could take the visa from the airport in UAE), so you have to show the Saudi embassy your position title on the Qatari Visa if isnt in the allowed list you have to make a visa from the UAE embassy.
hopefully i get the chance to help
Good luck