https://en.wikipedia.org/wiki/Times_New_Roman?st_source=ai_m...
This appears to be done by increasing the height of the lower case letters in the Times side while reducing the height of the capital letters at the same time. This then was also combined with a reduction in the size of some of the serifs which are measured against the height of the lowercase letter (compare the 'T' and the following 'h').
The Times is similarly readable at the smaller font size than the modern serif font - and scaling the modern font to the same density of text would have made the modern font less readable.
Part of that, it appears is the finer detail (as alluded to in the penultimate paragraph) - compare the '3' on each side.
I don't think that's the comparison you want to draw? The rows appear to hold very similar amounts of text.
But the rows on the left, in Times New Roman, are shorter than the rows on the right. So even though "one row" holds the same amount of text, one column-inch of Times New Roman holds more rows.
The Times New Roman looks more readable to me because it has thicker strokes. This isn't really an issue in a digital font; you can't accidentally apply a thin layer of black to a pixel and let the color underneath show through.