The price of the pizza goes to the restaurants, the delivery fee goes to the driver (mostly, I hope), and the "online convenience fee" goes to the business running the online ordering system. It all works out.
I don't think I've ever [edit: should read "recently", I surely saw some early ones that didn't] seen one that doesn't specify that the driver doesn't get the money. Presumably because when they (most pizza delivery places do this now, plus I think Jimmy Johns does it, probably others too) first started adding those fees some years back, people assumed it was for the driver and stopped tipping, since it's usually about as much as a decent tip would be.
Ever-rising, often-sneaky (different prices for delivery, much worse coupons for delivery vs. pick-up) increases in delivery costs have me thinking like my parents used to, and rarely ordering delivery anymore. There was a golden age in the late 90s and early '00s when delivery was pretty damn cheap, basically just $3-5 for a tip. It's over.