As a Desert Eagle owner...
Yes, it's truly gas-powered, compared to most other autoloading pistols. The gas port in the barrel is actually at the junction of the chamber and rifling throat, tapping off the gas pressure fairly early, then running it forward in the gas tube under (and integral to) the barrel and reversing to work the slide-mounted gas piston. The length of the gas tube and route it takes tends to slow down the cycling until well after the bullet has left the barrel.
The Desert Eagle is a big chunk of steel, no questions about it. It has an M16/AR-15 pattern bolt and barrel extension, with a solid lock-up. To cycle the gun, it does indeed need a good volume of gas pressure, so light loads are often the culprit to malfunctions.
Magnum Research actually has a webpage with recommended factory ammo that reliably cycles the big gas gun. If you handload, it's not too difficult to duplicate those factory rounds to ensure your gun works smoothly.
I have a .357 Magnum Desert Eagle, and it's even more fussy about the ammo it fires. Getting the gun to cycle at all with ammo less than 148gr is well-nigh impossible, and the previous owner of my gun gave up on it because he was trying to feed it 125gr JHP ammo. Since he figured it was a piece of junk, he sold it to me for $400 worth of computer parts. I'd been reloading .357 Magnum ammo for years on my Dillon Square Deal B, so it was no problem for me to make a batch of 158gr ammo that worked in the gun no problems.
H-110 is a darned good powder for the Desert Eagle, clean-burning and slow enough to move a big bullet with good gas port pressures. I use that, and also WW296 (Which some say is the same powder, different label on the can).
Remember, the big, heavy iron needs a big gas volume to cycle, kind of like a steam locomotive - not necessarily pressure, but *volume*. The .44 Magnum Desert Eagle has an easier time of it, thanks to the case volume of the .44 Magnum cartridge. But if you start reducing loads down closer to .44 Special performance, the gun will suffer.
Wildey and .44 AutoMag pistols are also pretty fussy about their ammo, for pretty much the same reasons. The LAR Grizzly and Coonan magnum autoloaders aren't gas-operated, so they need an ammo range that provides the proper recoil momentum to cycle their 1911-style actions.