Can you confirm that the whole trip is with Saudi Arabian Airlines?

They have different non-transit connected terminals in both Riyadh and Jeddah to foreign airlines which would require an entry stamp.

The disconnected terminals in Jeddah are particularly annoying.

Both airports are dull and you'll be climbing the walls to get out of the place.

As far as visas are concerned, you'll be at the mercy of whatever prick there is at your passport control counter, and if you get one of the nasty ones, also your nationality and/or ethnicity. Dress smart and smile glibly.