First of all, the story says Paddock was sold tracer ammo by the seller, not armor piercing which is what the seller got in trouble for selling over 100 orders of in several states. He didn't have a license to load AP rounds and that's why he's in trouble.
Tracer ammo, which is different than armor piercing ammo, has become popular just like explosive targets have with folks who like to see things light up and/or go boom. Lots of time they are used at twilight or after dark for the visuals. There were magazines found in Paddocks hotel room that were loaded with armor piercing ammo, but they didn't say anything about them being from the seller he bought the tracer ammo from and that they charged.
A box of 5.56 ammo is usually 20 rounds. So 720 rounds would have been 36 boxes of ammo in a large, heavy box, which I could totally see someone wearing a pair of gloves to protect their hands when picking up. Nothing suspicious. I probably would have done the same, as I have pretty soft hands. It's doubtful anything would have looked strange to the seller, surely nothing that would have made him call the cops as you suggest.
Each individual round is handled during the manufacturing process so the seller's fingerprints would have been all over them. Each round also has to be pressed in with a thumb when loaded into the magazines so Paddock's fingerprints, and the prints of his girlfriend too, who said she helped him load some of the magazines (though she knew nothing about his plans.) If the shooter was trying to keep his fingerprints off the ammo that would have been the time to wear gloves.
But, since he killed himself and made no effort to escape I'm guessing he planned this as a shooting/suicide and wasn't too worried about leaving fingerprints behind.
The cops just want the public to think their investigation is bearing fruit and stories like this make it look like they are, even if the arrest is pretty much unrelated to the Las Vegas shooting.