As pointed out, the mask does not have to be fully over both nose and mouth.
Correct. The mask
should be worn to cover the nose and mouth, but if mis worn as shown, it's still going to get the oxygen to the wearer.
To complete the thinking on this, it helps to understand that your average adult will take about 12 one to two liter breaths per minute. Of those breaths, 21% or so will be oxygen, and the rest the other components of the air, most nitrogen. While the overhead oxygen generator is providing near pure oxygen to the mask, that need and may only be 1/5 of the volume of air which the wearer would naturally like to inhale. So, if they inhale the rest of the non (or very low concentration oxygen) "around" the mask, the objective of providing the oxygen has been met. To this end, close examination of the "dixie cup" oxygen mask will show that in addition to a rather poor face fit, it actually has a rubber flapper valve for both in flow, and outflow. So, if a panicked passenger is pressing the mask tight to their face, those valves can open to assure that an adequate volume of air is being breathed in, in addition to the required oxygen.
But, yes, it would be nice if the passengers actually comprehended the passenger briefing, and wore the mask as it is designed to be worn!