Which was strictly the video feed from the first generation predator drones. If you look into the linked USAF docs, you'll see the actual telemetry and control channels are encrypted.
Wired is about as reliable about security reporting as Fox News is about the DNC. They know their audience, and want to sell eyeballs.
I am not sure how exactly I would do it, but my first approach would probably be almost purely mechanic.
Lets assume the drone is more or less blind to whatever happens above it as most of its sensors are pointed down and being stealth reduces its need to be aware of other planes (and forbids active radar). It should be feasible to approach it without being noticed and somehow entangling it (a net?) on its return flight, slowing it down (a parachute) until it runs out of fuel, and do it while jamming its communications so its owners won't have a clue of what's going on.
I think the worst problem is detecting it in the first place.
I'd expect it to be easier with a jet engine than propellers? Just use a steel cable net. Speaking of which, maybe if you use a close-mesh metallic net (maybe in addition to a coarse one for trapping), you'd break its uplink without any need for active electronic warfare?
All you'd have to do is to damage the propeller. A jet engine would probably run until there is no more fuel. I don't know how they did it, but, with the right incentive, any reasonably clever engineer would manage to do it.
It's a very unfortunate mistake to underestimate your opponents enough to give them your secret stealth drone.
The WP is a much more responsible and accurate article than Wired's sensational summary -- the salient points there are "Video is unencrypted", "Pentagon has tolerated this for years" and "Predator."
Getting back to the actual focus of my comment -- the original article leaps to "obviously, the Iranians have broken our encrypted controls" from an Iranian press release, without bothering to give even speculative support. I consider it far more plausible that something simpler has happened, such as dumb old software failure, or GPS spoofing.
Wired is about as reliable about security reporting as Fox News is about the DNC. They know their audience, and want to sell eyeballs.