IT is still not an arms race, as saudi and iran make no efforts to match eachother, and saudi has held m superior arms since the fall of the shah.
An arms race is more like what the soviet union vs america was, in constant aquisition of better tech and supply, or even ww2 where every nation tried to supply as well as engineer better than the other guy.
Iran has no need to get the latest or even more equipment, Iran and saudi fight through proxy, and in proxy fighting iran has the upper hand. Neither country will ever fight eachother head to head anytime soon. Iran has hezbollah, hamas, which they support to pressure israel to keep israel away from them, thev back houthis in yemen, which they use to prevent saudi expansion, and the have numerous shia militias they support which have been fighting isis and al quaeda/
Saudi has an almost non existent military reliant on us protection, and fights through proxy through isis and al quaeda, which is a risky idea, as both want to overthrow the saudi kingdom to install their own caliphate. Saudi though has american backing, so if isis and al quaeda ever win their fronts, and go back for saudi america would step in to protect them.