I think the point he's trying to make is that there is a skill gap, not a labor gap. We have plenty of people with degrees, but not enough with the skills they need to fill the jobs at hand.
If that were true, we'd expect to see wages rise.
Only those with valuable skills would see their wages rise, it is possible that the average STEM employee would not.
Depends, if a skill gap develops, you can then have a corresponding drop in productivity which can depress wages.