Because Square is not a MOTO processor, it's a card-present processor. You can't use Square to take payments on a website. The interchange fees for card-present transactions are less than 1/2 the average fees for card-not-present transactions. If they're paying 1% but charging you 2.75%, that easily covers the fixed fee you're comparing to.

They shouldn't be compared to PayPal, Stripe, etc. but to the standard merchant accounts brick-and-mortar stores get.