The definitions - whether one wants to debate it or not - are pretty explicitly spelled out:

Gentrifying Census Tracts: These lower-income Census tracts experienced significant growth in both home values and educational attainment. To be eligible to gentrify, a tract's median household income and median home value needed to fall within the bottom 40th percentile of all tracts within a metro area at the beginning of the decade. Tracts considered to have gentrified recorded increases in the top third percentile for both inflation-adjusted median home values and percentage of adults with bachelors’ degrees.


Tracts Not Gentrifying: These Census tracts met eligibility criteria, but did not experience enough growth in educational attainment and median home values relative to other tracts within a metro area to have gentrified.


Not Eligible Tracts: These tracts, typically middle and upper-income neighborhoods, did not meet the initial criteria for gentrification. To be eligible to gentrify, a tract's median household income and median home value both needed to be in the bottom 40th percentile of all tracts within a metro area at the start of a decade. Tracts with less than 500 residents or missing data were also considered not eligible.

Basically, they take the bottom-of-the barrel as those "eligible" for gentrification in their view. Gentrification can technically take place in just about any track; this seems to be a rather narrow definition weighted toward how far the lowest-of-the-low came along.