You asked if marginal tax rates impact prosperity. Of course they do.
I'm not sure what the point of your NY Times table is. All it shows is a comparison of tax rates. That doesn't even come close to answering the question of whether there is a connection to prosperity, and I assume you mean a country's prosperity. You imply there can't be much of an impact since Russia has a low 13% top tax rate and lower prosperity than all of the countries in the table. All of the other countries in the table, of course, have higher top tax rates. But clearly there are other factors that result in Russia's relative prosperity and lack of adherence to free markets in goods and labor is in my opinion at the top of the list. I would guess the marginal tax rate in Cuba and North Korea has almost nothing to do with those countries lack of wealth.
Are you asking if a country can be prosperous without rich people, or with fewer rich people or with rich people being less rich? I'm sure it can, but that's not the issue to me. From my perspective it matters what you want to spend the taxes on. If it's high-speed rail, subsidies for Solyndra, farm subsidies and the Ex-Im Bank, I say no.
The other issue to keep in mind is this. Taxes on the wealthy go down dramatically during recessions, mostly because capital gains become capital losses and that portion of their tax bill declines. When marginal rates change so too does the highly controllable amount of income a wealthy person will recognize in capital gains. Does that affect prosperity? I say yes. It reduces the incentive to invest in the latest and greatest. It's another reason growth slows. Growth equals prosperity.