Remember we in Britain get virtually no oil from the middle east - our oil primarily comes from Norway and Nigeria as well as significant amounts from other non-middle eastern countries - so we would have no interest in the oil outcome.
If Saudi were no longer pumping oil, we'd lose about 12% of the worlds oil production capacity.
If Saudi, Kuwait, UAE, Iraq and Iran were no longer pumping oil then about 35% of the world's oil production capacity would disappear.
So we
might have an interest as Brent crude would not be trading at ~$50/barrel!