In this example the fees capped were for outsiders who are buying things in the EEA. e.g. an American buying something from an Italian vineyard or an Australian buying some authentic British tableware (for now).
The EU also forbids hidden fees for most types of transaction. It wants the advertised price to match the price paid by consumers‡. If I have 25 EUR in my pocket and you advertise a product for 25 EUR I should be able to get that product. Whereas in the US if you see a product advertised for $25 you know they'll want maybe $30 or more as they add fees, taxes and charges on top of the supposed price. As a consequence this means the fee for a card ends up built in to most online prices in Europe, even if you actually transact in some other way that reduces or eliminates the fee for the seller. So ensuring the fee is low makes good sense here too.
‡ British supermarkets (used to?) use a trick to reduce taxes here - they charge you a fee for their backend card processing, but they subtract that fee from your checkout price. The cost to you doesn't change, and you'd never notice unless you read the small print, but they've successfully argued that this service fee should be taxed differently than your purchases, saving them money. Since it doesn't affect the headline price versus price paid the EU doesn't care.