The score seems to be based on the number of countries you can enter without a visa.
This is pretty meaningless as countries like St. Kitts and Nevis (Caribbean, population 47,000) and China are treated as the same.
Edit: Searching around, this (2018) is exactly what I had in mind--travel freedom + settlement freedom: https://www.nationalityindex.com/
ESTA/ETIAS gets automatically approved within a few minutes of paying for the fee (I guess this is true for 99.999% of applicants).
Very few countries allow people to just show up and cross the border. US citizens had that privilege in a lot of places, but it looks like it’s changing now.
That is not true of schemes like ESTA or ETIAS.
Some countries have visa-on-arrival schemes, which are the opposite of ESTA and ETIAS. The visa still exists as a formality (maybe due to reciprocity or as a tourist tax), but you need to do little beyond paying the fee to get one.