I was a lifeguard at Barton Springs and at UT for years. Also trained lifeguards for COA. I probably pulled 15 or 20 people out of the water in my time. That guy was a textbook case of a distressed swimmer/active drowning. Absolutely no reason those "lifeguards" should not have been on that guy like surlyites on South Austin's mom. That video will be used in lifeguard training videos for years to come.
And yeah, they probably weren't actual trained and certified lifeguards, or they would have had rescue equipment, as Smuggs pointed out. It takes a specially trained and strong swimmer, even with rescue equipment, to pull a 200 pound slab of beef with no buoyancy off the bottom when they are 10+ feet down. Add in the fact they guy was obviously conscious when he went under, (which means he's going to be grabbing onto you if you let him), and you are in a world of shit if you don't have a rescue can/tube. Which is why you save them BEFORE they go under.
Not only should those paddleboarders have been lifeguards, they should have been the best of the best: trained and experienced and certified in open water guarding with competition level swimming abilities. I guarded a few private gigs in my day, (triathlons and open water swims and such), and if the person hiring me had told me I'd be on a paddle board in a fucking lake with no rescue can, I'd have laughed in his face and noped right the fuck out of there.
I will say that paddleboards are not a bad idea in that sort of situation-- the guards can be close to the swimmers, and once the victim is saved, the guard can pull him back to the board instead of all the way back to shore. You can even load the victim onto the board if they are too weak to hold on or unconscious.
edit to add: Two guys drowned at Balmorhea earlier this summer. Old dude went under, son in law jumped in to save him (I'm guessing no lifeguard training), and he drowned also.