First off, I'd weight countries that grant visa-free access to relatively few other countries (e.g., China, USA, ECOWAS) more than countries that are comparatively more lenient (e.g. countries like Samoa, Tuvalu that grant visa-free access to everyone).
Secondly, I'd additionally weight for residency mobility - the ability to work and live in another country with few conditions (e.g. Schengen area, Common Travel Area, Trans-Tasman Travel Arrangement, MERCOSUR, ECOWAS, CARICOM, Freedom of movement in the Gulf States). Countries like Canada, Japan and Singapore may score well on paper for travel mobility, but are definitely weaker than EU passports that allow you to migrate to where jobs are and improve your own economic outcomes.
If you read the actual article, it seems a US passport is about as good as it always was. It seems like much of the change is various countries expanding visa free travel, just not to Americans. Before when I went to China or Vietnam, I had to get a visa. Now with this change in ranking...I still have to get a visa.
What if I do? Is this index only for US citizens to make use of?
"Important" in this way? At least by the current methodology, it's fairly bias-free, which if you add "Countries that are more important than others weight more" to the mix you cannot call it bias-free anymore.
edit: it _SHOULD NOT MATTER_, but I grew up in Turkey, am half Persian, and am very liberal. If that matters to you, please think good and hard about what kind of person you have become.
edit: here's the number of US visitors to each country in 2018 (the easiest year for me to find data on). This isn't a perfect comparison, because the amount of visitors will of course depend on the visa situation for each country, but it does give some feeling for how useful increased access would be
Barbados in 2018 had 204,830 US visitors -- https://www.caribjournal.com/2019/03/11/american-travelers-a...
China in 2018 had 2,485,000 US visitors (but this may be padded by the state media) -- https://gowithguide.com/blog/exploring-china-s-tourism-lands...
So China attracted approx 10x more US visitors, even though in 2018 it was much easier for Americans to go to Barbados than China. And I bet that gap has only grown in the last 7 years.
https://www.eternalandamans.com/havelock-island/radhanagar-b...
https://www.gokitetours.com/top-beaches-in-lakshadweep-you-m...