I clicked on the original paper: the authors are basically conflating IT and STEM. IT is clearly flat, but the rest of their is less clear.We're pretty clear on why we look at IT in the second half of the paper: the lion's share of high skill guestworkers go into IT. The inspector general of DHS called the L-1 "the computer visa". So after going over the STEM graduation numbers generally it made sense to look at IT specifically in relation to these visas. There's no conflation at all. We know they're different. If you're interested in the impact of these programs, look at the labor market where the programs are supplying workers.
Although this is anecdotal, the engineering school our our college is boasting that 90-95% of this year's graduating engineers already have their career jobs lined up a month before graduation...
As for other fields, we've looked at that elsewhere (and cited the work in this report). Some are doing better than others. The life sciences are very glutted and have been for a while. The health sector (if you consider this STEM - definitions vary) is inhaling workers right now - it's doing fine. Other engineering fields we've looked at experience temporary shortages during the adjustment process. People find this in the literature all the time - run ups in wages due to positive demand shocks that take time to erode away because it takes students a few years to work through the educational system. In other words, the short run supply curve is inelastic and the long run supply curve is relatively elastic. A good recent example of this is petroleum engineering.
So not all fields are as glutted as the life sciences, but no study that I am aware of has turned up a finding of chronic shortages in a STEM field. Why? Because people respond to incentives. These are specialized fields so you can get a glut of workers with certain STEM skills, but it's very hard to find any evidence of chronic shortages.
As to his last point, that's a remarkable case. I don't have the employment rate for engineers out of college on hand. The non-employment rate is low but would still take up a good portion of his remaining 5 to 10%. Of those who do get jobs a year out of graduating, only 53% of engineers are working in engineering (the balance may be out of the engineering field by choice of course). These are not necessarily career jobs, but you'd think engineers would be considering an engineering job to be their "career job". So the idea that 90-95% of a class have career jobs before graduation is an enormous outlier. Maybe it's true, but it's not typical at all. Schools are notorious for gaming these sorts of numbers - I'd err on the side of not trusting it.