It is somewhat dated. For example, Adam Tooze's research into the Nazi economy for Wages of Destruction indicates that the idea that it wasn't until 1941-42 that Nazi Germany under took a shift to a "total" war economy is incorrect. There was a fair amount of rationalization that took place under Speer, and even before under Fritz Todt. His suggestion, also, that the Allies fought on knowing their cause was just and the Axis didn't is tenuous at best. Although there should be no doubt that most servicemen were aware of why their countries were fighting, recent social history of Nazi Germany (including Nicholas Stargardt's excellent book The German War) indicates that people in Germany rallied around ideas of German nationalism, and around Hitler as a figure, and that support for Nazi ideology was not a necessity when supporting the war effort. This combined with coercive measures as the war went on ensured that resistance to the Allies was fierce up until the spring of 1945, although ultimately futile.

There are some other examples, notably his portraying of the German advance after Barbarossa as nearly succeeding, and of smashing Soviet armies with superior numbers and equipment. David Stahel's work on Army Group Center, and also David Glantz's book Stumbling Colossus indicates that command and control, morale and unit cohesion were greatly deficient in the Red Army units facing the invasion, and that much of the aircraft and AFVs they had were obsolete. The Germans did employ their forces well, but it's hard to see how the Red Army could have conducted an effective defense, even more so when one considers that they lacked border fortifications (which were back at the 1939 border), and were prevented from acting on intelligence by Stalin. That said, the Germans were hardly close to capturing Moscow, given the poor weather in autumn-winter, the abysmal state of German logistics, and the heavy losses that had been incurred earlier in the campaign.

In that sense, it was a combination of Axis failings and deficiencies, and Allied defensive efforts on land, in the air and at sea that halted Axis expansion. By 1942 at least, the chances of Germany attaining it's grandiose war aims were almost nill (if they'd ever had a chance), and the Japanese were already being checked and reversed at Midway, Coral Sea, Guadalcanal and in New Guinea.

That being said, I'd say his general argument remains valid. The Big Three were economically superior, with greater production capacity and population than the Axis. More importantly, they organized more effectively their economies, and pursued coherent war aims and policies for the most part. Furthermore, his point that solid leadership, command and control, elan/morale and coordination of forces on the battlefield are necessary if materiel superiority is to be used effectively is, at least I'd say, valid as ever. While the Axis may have been unable to achieve their war aims after 1942, the Allies still had to achieve theirs, and this meant coordinating and formulating strategies, and sending in armies that were armed, equipped and led well enough to decisively defeat the Axis. Even if they couldn't achieve their aims, the Axis, especially Germany, could still conduct a defensive campaign that would be drawn out and costly, and at least force a peace of exhaustion. The Red Army had suffered heavy losses in 1941-43, and while their operational and tactical methods greatly improved by 1944-45, and casualties were lower (though they remained annually in the millions), victories like the Dnepr-Carpathian Offensive and Operation Bagration did matter, as they weakened the German Army and forced it to abandon territory that it could otherwise have ceded at the price of a hefty butchers' bill for the Red Army. Likewise with the Western Allies; the British took time to settle on effective combined arms methods, though achieved this under Montgomery's command, while the US Army face a similar learning curve, whileb preliminary campaigns like the Battle of the Atlantic, the Bomber Offensive and the Invasion of Italy had to be undertaken before Allied military and political leadership felt prepared to risk an invasion of France and Europe proper. Although they were by no means perfect (neither were the Axis), the Allies were able to mobilize their economies and militaries effectively, and by 1943 at least were conducting campaigns that played to their advantages.

TL;DR: It is somewhat dated, and the economic and moral aspects of his thesis are flawed to varying degrees, but it's still a good read, one which makes a valid point about how the Allies were able to attain victory.