It says (roughly) "Payment cards without fee: All Danish and foreign debit cards"
"Payment cards with fee: 0.9375% Danish issued; 1.75% foreign issued."
I know there are extra fees for business/corporate credit cards, and these are specifically excluded from the EU cap. (The cap was for consumer protection, so business transactions aren't regulated.)
Foreign (non-EU) fees are also not part of the EU cap, as there's no way to control those.
It could be poor wording on the sticker, or it might be including the other fees. The 0.3% is just Visa/MasterCard's fee, there's also the fee from the card processor — HN is familiar with Stripe, but there are many companies offering this.
People trying to get air miles, cashback or similar have to pay the cost of that.
Don't most people have the normal visa/mc debit cards there?
That was pretty much specific to German-speaking countries (or at least they were the only one, where I noticed that). Elsewhere, there was no such thing as ATM-only card (or even ATM-only PIN).
Don't even exist in many places anymore. e.g. in the EU country where I live both were replaced ~8 or so years ago by Visa/Mastercard Debit (since they removed embossed characters the only way to distinguish them is the word 'debit' written in a tiny font.
I assume there's gradually less and less appeal for a card that isn't as broadly accepted, and if it encourages more fee generation, all's the better.