I don't see why it's supposed to be illegal to pay someone to pick something up for you. Be it a bottle of Tylenol from CVS or some to go food from the local restaraunt. If the person goes there and finds out the restaraunt doesn't have takeout it's irrelevant to that.
It's obviously wrong to pose as/support fake versions of businesses or present yourself as contracted by them for delivery when you're not. Unfortunately the article has neither the wording nor information to make it clear which is actually going on. I suspect both to some degree though.
This is why it’s not okay to just let GrubHub/etc. add restaurants to their apps without the restaurant’s explicit permission. Getting takeout food isn’t like picking up a bottle of Tylenol - takeout orders require plastic containers and silverware and often take longer to prepare. Not to mention the fact that restaurant kitchens are already quite busy and don’t want to spend time figuring out some third party’s mistake.