point of fact, the Russians replaced the AK-47 in the late '70s/early '80s with the AK-74, an updated design (also by Mikhail Kalashnikov) chambered for a then-new .22-caliber cartridge, the 5.45x39mm--much flatter shooting, even less recoil than 7.62x39mm, and better terminal ballistics in military FMJ loads (contrary to the tenor of the OP, the 7.62x39mm with military FMJ loads isn't as lethal as its reputation would suggest, with wound profiles often similar to 9mm FMJ). The AK-47 has been considered obsolete for front-line service for nearly three decades now. The author is right, though, about the design's ruggedness and reliability, and those traits were carried over into the AK-74.
I too own a civilian AK lookalike in 7.62x39mm (real AK-47's are VERY tightly controlled in the U.S. by the Title 2/Class III provisions of the National Firearms Act, so my SAR-1 is non-automatic). The thing that strikes me about the design is how well it was thought out. The safety lever (fire control selector on a real AK) covers up the charging handle slot when the safety is on (as in the photo below), helping keep dirt out of the mechanism. The long-stroke gas piston/bolt carrier was a stroke of genius from a reliability standpoint, and there is enough room inside the spacious receiver for dirt and crud to move out of the way. The magazines are built like dump trucks (the steel composing the magazine feed lips is maybe 2-3 millimeters thick, compared to maybe 0.5 - 1 mm for U.S. designs.
Romanian SAR-1, U.S.-legal civilian AK lookalike (non-automatic), 7.62x39mm
Downsides of the design--safety lever can't be reached with the firing hand unless you have LONG fingers; either you reach under the rifle with the support hand to flick off the safety when ready to shoot, or you remove the firing hand from the handgrip to do so. Western guns more typically have safeties/selectors reachable with the thumb or index finger of the firing hand. The AK (even the -74) has no bolt-hold-open and a rock-and-lock magazine catch, so the gun is slow to reload. The rear sight is further forward than it really should be (too far from your eye), but that's a compromise of having a long-stroke action with a removable receiver top cover.
As far as whether the AK-47 is superior to the M16--in Iraq, in straight up insurgents-with-AK's vs. Americans-with-M16's firefights, the AK is almost always overmatched; an M16 with optics allows you to engage an AK-wielding person at ranges well beyond the AK's ability to easily hit. BUT, the M16 has to be kept scrupulously clean, or else it will malfunction in the dusty/sandy environment (as Jessica Lynch's group found out).