Inflation can be increases in prices, and it is used in this way by most modern economists, except hard money economists to whom inflation is by definition the increase in money supply irrespective of prices. In this sense, inflation is what causes price increases but isn't price increases. The article is talking with this second, or original definition of inflation.
Inflation is calculated from the increase in prices. It's a measure of the drop in buying power post facto. The earlier definition is incomplete as it does not take into account velocity. For instance, if you print a $1T coin and hand it to me, then I throw it into a vault, supply went up but nothing changed with respect to prices, because velocity went down commensurately.
The earlier definition does not match observable reality.
That is only because what you are interested in IS price increases.
If what you are interested in is money supply, and you call that inflation, then it doesn't matter what you do with the money, you can store it, you can burn it, you can spend it, is all the same. It doens't matter if prices go up either, that is irrelevant under this definition of inflation.
Inflation used to mean money supply. Inflation now means price increases.
People thinking they are talking about the same thing when they use the word inflation is where the confusion is coming from.
The issue is that inflation as a function of supply alone is an incomplete model, not particularly meaningful and has been long-since debunked. Trying to resurrect an incomplete model isn't a great idea IMO.
Inflation shows how much prices have risen in a given year, not how many new dollars are in circulation.
You can measure inflation in the US economy using any currency - gold, USD, BTC.