That example looked to me like 'if both cars arrive at the same time'. In that case, straight has ROW.
If the left-turning car arrives first, it has the ROW, assuming both cars don't have a really long wait at the stop sign. Then, it could be common courtesy for the straight car to go first as they might have an easier go of it. But I think the left-turn car still technically has ROW because they arrived first.
The best course is to use your judgement, be courteous and probably also signal or communicate to the oncoming car if you can that you are either going or letting them go first.
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