From the people I've spoken to about tarpon fishing from kayaks, fighting the fish is certainly doable, and can tire them out more quickly as they pull you around than from shore/boat.
You gotta be kidding me! That is absolute nonsense.
It took this guy, by his own admission, over 3 hours before he was able to get a decent tarpon boatside. Listen to his buddy's words as they finally get it close after over 3 hours of battling a tarpon on spinning gear. It is less than 3 MB and 2 minutes.
Here's an article about another 3 hour battle. The fact that the guy was able to lift that fish halfway into his kayak without gloves indicates that the fish was so near dead it couldn't even wiggle. Tarpon are the slimiest fish in the ocean and hard to hold by their lower jaw even with those yellow gloves on if they have any strength left at all.
Kayak Angling for Big Fish: Tarpon by Kayak, Paddle for Your Life! 8-13-11
Neither of those fish would have taken more than half that time to land from a boat with a proper fly rod by even a first time tarpon fisherman with some good coaching.
Even with one or two other kayaks adding more drag to that of the hooked up angler's kayak, it will still take longer to land than from a boat with motor. But it can be done with at least a chance of saving the fish, assuming the other kayakers will tow the fisherman in an effort to revive it.
So, if you go tarpon fishing in salt water from a kayak, go with some other kayakers so you have a chance to shorten the fight time and revive the fish afterwards. And make sure you all have ropes for the towing. Your buddies could be in for a lot of paddling.