I travelled KWI-JED
and can confirm no Visa is needed. Actually I found SV
airport however is a simple affair. You'll be bus boarded to arrivals. Directly after stepping into the building, there is a transfer desk, You will need to approach this desk, no matter if you already have your connecting boarding pass (which I had) or not. They will issue you a meal voucher.
Then they send you upstairs. There you pass through security (male and female separated). That's it. Once you're in the waiting hall, there is really nothing but a duty free ship and this food stall where you can use your voucher.
If you have a long layover, I strongly recommend you pay entry (some 20 EUR or so) for the SV
Al Fursan lounge. It's nothing special, but they have decent food and wifi as well as computers you can use. bring a pullover, they really have cold air condition!
If you have an insreali stamp, even though in transit, I would be very cautious though. On departure in JED
before boarding the bus to my transfer flight, security staff checks every passport for stamps.