"So rapidly the power of your initial attack runs out. And then the counter-attacks, as inevitable as the rising sun, start. Your opponents can shell you from nice, prepared positions, while your artillery now has to move forward to support you. Their troops can ride railways to staging posts close to the front lines, advance through well-maintained communications trenches directly to you, while your troops have to advance over open group, under artillery fire, in order to support you."
The cause of the WW1 stalemates was not artillery, but asymmetrical mobility capabilities on the attacking and defending sides of any offensive. During the war the various armies, as stated in the article, got really good at the first phase of an attack: breaching the enemies front line. They were not always good at this (see Somme, 1916) but they got there through refining their use of primarily artillery. However, what they could never solve during the war years was the problem of what to do to push an attack forward, and this was caused by mobility problems. The attackers had very limited options when it came to the attack, and it was almost entirely men walking forward. This limited both speed and endurance. No many how many men you had if they all start walking from the same place they can all only walk so far before they need to sit down for a bit of a break. There was no way to expedite this process because the technologies that would allow it either did not yet exist (reliable and powerful ICE) or could not be pushed forward fast enough (railways). The limitations of a person moving forward on foot meant that at some point the initial impetus of the attack was going to end while reinforcements caught up, and that is where the problem was.
While the attackers were struggling forward on foot the defenders could use a fantastic technology: railways. Reinforcements could be rushed in from almost anywhere to counter the attack that was developing. Then when they arrived at the railheads they could move to the front line and begin launching counter attacks near their own sources of supply and against an enemy that had just walked themselves into exhaustion. This advantage was most strongly felt in the very well developed and confined areas of Western Europe where both sides (Germany 15, 16, 17, Entente 18) would be able to move around troops very quickly. On the Eastern Front this advantage was less apparent because of the less developed transportation systems which put the two sides of an attack on more equal footing.
Artillery was really good at solving the first problem (tactical breakthrough) but really bad at solving the real problem, how to continue an attack. This problem was just made worse by the long artillery preparations of 1915-1917, because the various armies were broadcasting to everyone where precisely they were going to attack, giving them a very long time to prepare. These preparations could not prevent an attack from occurring, or it being initially successful, but it could always prevent an attack from transitioning from battle of attrition to battle of movement.
This turned into a bit longer of a post than intended, and I do want to reiterate that I do like this article and I think its only flaw is that it does not follow its own logic one more step.