Wouldn’t companies with a strong international presence (e.g. Apple) contribute to that? It seems like increased globalization could explain that high ratio rather than “overvaluation.”

That would be counted in America's GDP.

The metric as designed is more flawed, because not all companies are public.

Exports contribute to GDP but sales between foreign subsidiaries do not. So a Toyota made in Toyota-owned Kentucky factory contributes to the US GDP. This is in contrast to GNP; that US-made Toyota would count towards Japan's GNP.

Is the value of stock supposed to equal the GDP?

It is my understanding that the value of a stock should be equal to present value of future cash flows. If those future cash flows are growing faster than the discount rate then a value higher than 100% of GDP is to be expected.

Agreed. I've never come across this particular metric before, but intuitively I would have expected something more akin to a P/E ratio in the 10's or even 20's, not a factor of 1x.

Can anyone explain here why the stock market cap isn't much, much higher than a single year's GDP?

Is it because GDP is essentially "revenue" while market cap is "discounted future profits" -- and thus 20 years of 5% profit is going to be on the same order of magnitude of 1 year of revenue?

There are only ~5,000 publicly traded companies in the U.S. There are about 25 Million small businesses in the U.S. The stock market cap represents a tiny portion of the entire U.S. economy.