Saudi Arabia is playing its own game. Yemen and Syria are SA losses ofcThey have lost in Syria years ago. The rebels still holding today are backed by Turkey, or US, not the Arabs.
I don't think the deal means that anyone is giving up Yemen. It is a cease fire right now. The deal only means that they will not resume fighting and should negotiate.
Iran is getting its own money frozen by US. It has nothing to do with Saudi. Trade is bilateral, Saudi is not obliged to trade with Iran if it does not want to.
Remember Saudi is not more innocent than Iran in the rivalry, both sides stopping or halting the confrontation are what both sides get. Saudi does not deserve more than Iran.
MBS was young and inexperienced at that time and he got carried away thinking that there was a strategic opening for SA to make gains. Well he wasn't wrong, there was indeed a big strategic opportunity for SA at those times.
What MBS got wrong is that he overestimated his military and country's power, and that's how Iran turned it around against SA. Recent years it seems that he has gotten some of his brain back and he is making shrewd moves though.
As for Iran, the less said about them the better. Their international influence has hit its peak but its national comprehensive power has hit rock bottom, they are in a huge mess internally.
So Saudi Arabia and Iran have probably realised that this past decade has been an overall mess/loss for them and, probably, with China's encouragement, they are willing to try a new approach and turn over a new page on their messy situation.
Saudi Arabia's purpose on this deal is clear. Vision 2030. Diversify, grow your economy as much as possible, build local industries, MIC etc. When 2030-2035 comes, let Iran see that making trouble with SA ain't worth the risks. So what MBS has to do in the meantime is to sit tight, make peace and friends with everyone, and basically play the dumb kid in the school. Basically, they are trying to copy China-style with their own Saudi Arabian characteristics slapped on top