Well, magical abilities I dunno about, although I wouldn’t be surprised if the Gardeners had a bit of the Fisher King fertility god going on.
To begin with, I love that the truly successful Gardener kings are not the warlords like “Garth V (Hammer of the Dornish), Gwayne I (the Gallant), Gyles I (the Woe), Gareth II (the Grim), Garth VI (the Morningstar), and Gordan I (Grey-Eyes).” A lot of those guys ended up very very dead, usually at the hands of the Ironborn (interesting that anti-Ironborn sentiment isn’t a bigger thing in the Reach).
Rather, the really successful Gardener kings are the politicians like Garth the Great, who established the northern boundaries of the Reach with mutual defense pacts, Garland the Bridegroom, who married into House Hightower and brought Oldtown into the Reach after Gyles the Woe failed to sack it, Gwayne the Fat who brought the Peakes and Manderlys into the realm peacefully by acting as a fair judge, and John the Tall, who expanded the Reach through trade and exploration. And when you look at how the Gardeners reacted to the Andals, it’s a complex mix of military preparation, cultural adaptation, intermarriage, and recruiting, so that by the time that the Andal kings attacked the Reach in force, the Gardeners had Andal knights and Andal lords ready to fight them.
And of course, you have Garth the Goldenhand, who’s an underrated memetic badass. Here’s a man who handily whups the Ironborn and the Dornish, then turns around and defeats an alliance of the Westerlands and the Stormlands through espionage and psychological warfare, then convinces their kings to marry his daughters and sign a peace deal that gives the Reach everything it wants, who rules for **81 years,** with more than 70 of them going by without fighting a war, and dies with all of his marbles intact. If Jaehaerys is the best king that the Targaryens put up, Garth the Goldenhand might just be the best monarch in Westerosi history.
At the same time, though, you definitely see that House Gardener got hit by a bad case of victory disease. They were so rich and so powerful that they tried to grab all of it – hence Gyles III trying to conquer the Stormlands and fighting the Reach and the Dornish and the Riverlands at the same time and getting a lot of people killed for nothing, leading to the civil war that almost ended the Reach during the reign of Garth X.
But then, you have to be impressed by the resilience of the Gardeners. Despite losing land to the Westeralnds and the Stormlands, despite having the Dornish sack Highgarden, burn the Oakenseat, and kill their king, Mern VI and his Tyrell advisors manage to win everything back, just in time for Garth the Painter to wreak such a terrible vengeance on the Dornish that he painted the Red Mountains green.
In short, I find the Gardeners both a fascinating example of but also a complete undermining of the entire chivalric culture of the Reach, permanently poised halfway between the seductive and deadly appeal of la gloire and the patient, hardheaded work of realpolitik.