I have not gotten into mountaineering so have no experience with pulse oximeters for that.
In a brief search online it appears they are used to determine how well someone is acclimatizing to a given altitude. I suspect the outfitters have a lower limit of oxygen saturation that must be maintained before a client is allowed to continue going up the mountain. And if the oxygen saturation is below that level, the client is taken down to a lower camp.
http://www.high-altitude-medicine.com/SaO2-table.html