There's a fair amount of confusion between map and territory in this article. It seems to take macroeconomic indicators like CPI, nominal wages, and real wages as fundamentals and then infer that the economy must behave a certain way because of historical relationships between them, when the reality is that the economy behaves as the economy behaves and the macroeconomic indicators only measure what's going on.

A good example is "By definition, inflation-indexed wages cannot result in a higher inflation rate. Wages indexed only to inflation will actually reduce the inflation rate, if productivity is positive, which it typically is." No - if you have an inflation-indexed wage, it will go up when inflation does, regardless of what productivity does. You can't just infer that productivity has risen because the inflation-indexed wage went up - in this specific instance, it's clear that it hasn't, because nothing has changed except the inflation index.

Inflation is best thought of as a feedback loop. Every expense is somebody else's income, so if expenses are going up across the economy, somebody is getting more money. That gives their suppliers leverage to raise prices and their customers a need to raise prices or go out of business. The rate is going to be uneven across different sectors, which is where the CPI vs. nominal vs. real wages behavior comes in. Real wage increases are nominal wages * CPI, by definition, so if most of the increase in prices is accruing to labor, real wages will be positive, while if most accrues to capital, real wages will be negative.