How does it enable large discounts?

@AbsolutelyNotAVelociraptor@piefed.social guessed it. Grocery stores frequently sell Disney gift cards. Grocery store loyalty programs give a multiplier of points for gift card purchases with redemption in dollars-of-future-groceries-for-free or gallons-of-gasoline-for-free. This is worth usually about 10% of the cost of the gift card. Meaning, buy a $100 gift card, and get $10 in groceries/gasoline for free. Additionally some credit cards give large bonuses for grocery store purchases. The American Express Blue Cash Preferred is the best one I know which gives 6% cash back on grocery purchases. So on a $100 Disney gift card purchase, that's $6. That's where you get your minimum of 16% discount. Sometimes the grocery store points programs have promotional periods where even more points are earned for specific vendor's gift cards (or category of gift cards). This can increase the free groceries or gasoline up to occasionally 19% back. Stack that with AMEX, and you're spending $100 for a Disney gift card but only paying $75 for it.

They’re doing this because people found a way to pay them less as long as it’s through a gift card?

I doubt thats the reason, but it is a consequence to myself and others that use this method.

In the past all merchants in Disney Springs were required to accept Disney Magic Band payments for any item sold in Disney Springs (which if you don't know is just a large outdoor shopping mall of regular mall clothing, novelty, athletic wear etc stores). The infrastructure needed to take a Disney Magic Band at the Point of Sale in a store was a specific terminal with a Disney specific RFID reader. That same terminal has a magstripe reader which accepts regular old Disney gift cards.

What I'm guessing businesses hate, is having to deal with the magic band terminal. Most stores I saw only have one of them, they are a bit temperamental, and very very few people use it which means its only available at one cash register, and staff training on it is very thin because it is so rarely used. In short, its a lot of overhead to manage and maintain burning up expensive human labor for something that doesn't drive a profit. So with the coming expiry of the contracts requiring Disney Springs merchants to provide the service, a handful of semi-powerful merchants said "we don't want this anymore" and Disney agreed with them.

I'll be sad that I may not be able to get Zara, Superdry or Uniqlo at deep discounts anymore though.

My guess is that you could probably buy a $100 card at a discount paying it maybe $80.