In that book Greenblatt goes on to discuss various weighting schemes, result:
Cap weight < equal weight < fundamental weight (e.g. RAFI) < Greenblatt's "Value weight" (low price/high ROC)

That is what he espoused in a couple of his books. Nobody has been able to find performance in the data anything like what he claimed as is valuation formula, but that's life. Fundamental weight is superior to cap weight in that it doesn't allow overallocation based on overvaluation, but I personally don't see the reason to invest more of my money in bigger companies. Yes, the market as a whole must do so by construction, but I don't.

I'm confused about "factor" vs "quant" (or mechanical) investing. Isn't factor investing an application of quant methods? For example, you find companies with high ROE have tended to outperform on average, which makes sense, then select a portfolio of stocks using that "factor". Isn't this what the factor investing industry is doing?

The terms mean pretty much the same thing. The term "factor" normally has the connotation of studies done long ago that purportedly showed that there were only very few factors that explained most variation in stock returns: small stocks doing better than big ones, value stocks doing better than growth, momentum having some merit, etc. I think there were four in the original papers. Quant investing is simply investing based on anything you could write a program for: fundamental quantities and/or price/volume figures. But in the most general sense, anything a quant strategy uses is a factor. The confusion comes about because some traditionalists assert that quant strategy XXX is working only because it has a bit of one of the old four factors. (earth, air, fire, water?) It's worth noting that the "small beats big" factor was never really a thing, according to some newer research, it was mostly about liquidity. Personally, my two favourite dumb quant criteria (factors?) are ROE and sales growth rate. One quant criterion that has worked very well in recent years is upgrades to forward earnings estimates.

Jim