[Sniffnoy]

No. What they actually do is that they do a regression with both X and Z among the independent variables, and then look solely at the coefficients coming from X. (As mentioned in the article.) Including Z as a dependent variable alongside X "controls for" it in that now the coefficients for X are supposed to not include any effect from Z (since any Z effect should go in the Z coefficients). How well this works is something I don't know enough to answer.

I don't actually know how the method you suggest compares in the limit of finer bins. It's possible it might only achieve similar results?

[KempyKolibri]

The smaller bins approach is adjustment via stratification.

Good primer on both here: https://www.mynutritionscience.com/p/statistical-adjustment

[youainti]

My understanding is that in the limit, it does the same thing, but with more of a flattened tree representation.