This is the crux of the article's argument, and I disagree. In a shortage, employers would need to raise compensation, not necessarily wages, to attract workers.
(a) You're missing my point. The study cites hourly wage data for years 2009 through 2014. How large, or even how common, were sign-on bonuses (not perf bonuses) in 2009, and what are they at now? Sign-on bonuses are trivial to value. Any fair study would make an attempt to include that data - this one doesn't.
(b) How common were were shuttles, day care, onsite yoga/fitness lessons, gender reassignment surgery, egg freezing, and whatever else in 2009? These things do have some value - to me at least, it's the amount of post-tax money I would have spent for these amenities elsewhere. People are unlikely to use all of the benefits of course, but the basket has grown.
Health insurance as a benefit can't be considered to be a "basic requirement" and ignored, since plans vary a lot in coverage.
(c) While the stock of "most companies" might be worth nothing, those companies tend to be small and short-lived. Regardless, the majority of engineers work at larger established companies, and most of those working at a startup that might fail in a month are doing it out of choice.
TL;DR I am making an argument against the merits of the study. Rise in total compensation, and not rise in wages, is what matters.