What is this statistic measuring? Number of adults who have some form of Visa card? Number of transactions in total? Online transactions? Debit and credit cards combined? If you're able to provide more detail that would be useful.
According to the industry, debit card usage far outstrips credit card usage, at a ratio of about 3:1 for online purchases[0] - and debit cards were unaffected by Amazon's proposed change. So if we assume the 3:1 ratio holds true for Amazon customers, then we're looking at an absolute maximum of 15m/4 == 3.75 million customers - i.e. if all of them are paying with Visa.
Five years ago it was reported that MasterCard had 65% of UK credit card market[1]. If we assume that hasn't shifted much, and ignore Amex and other issuers (i.e. granting Visa a generous 35% market) then we end up at 3.75m*0.35 = 1.31 million customers, or about 8.7% of Prime subscribers. A big and valuable chunk, to be sure - and obviously Amazon's customer base could well skew towards Visa for some reason or other - but to me it still isn't anywhere near as dramatic as "Visa has ~80% market share" implies.
[0] https://www.ukfinance.org.uk/sites/default/files/uploads/Car...
[1] https://cmspi.com/eur/blogs/competition-in-the-debit-card-is...