The article only talks about the currency used in its reports. It means, if the Central Bank of Iran issues a report, the figures will be not be given in US$ but in another unit (for the rest of the answer, let's assume EUR even if the article cannot answer that issue).
So, if official economical organs of Iran issue a report stating their reserves in foreign currencies, it will say EUR X€ instead of US Y$.
The article explains that Iran makes little business using US$, so its reserves are in other currencies. This probably causes that the reports are inaccurate due to the variations of the exchange rate.
For example, imagine that I have of EUR 10.000 and current US/EUR exchange is US$ 1 = EUR 1. So I issue a report stating that I have cash for the value of US$ 10.000, and it is correct right now. But if in a month US$ 1 = EUR 2, now my report is off by a 50% because what I actually have are EUR 10.000 valued at $ 5,000. The less US$ I actually have, the more risk of inaccuracies (either positives or negatives) I might suffer.
So the CBI is of the opinion that it makes no sense to report its data in US$ while what they have (and will use for trade) are EUR and other currencies1.
And even if Iran decided to only accept EUR2, that would not make much of a difference. US$ and EUR are fully convertible, anyone wishing to buy something from Iran would only need to do the conversion, and the actual number of trades with Iran in US$ is already very limited.
A different issue would be if the rest of the world decided somehow to stop using the US$ as one of the common currencies for trade and foreign reserves. This use increases US$ demand so, as long as international use of the US$ increases, the USA (and other reserve currencies) gets goods "for free", just in exchange of printing money3 for people who want to use it as reserve or for buying other goods in international market. But the article has nothing to do with that.
Note that, from the
Forex Reserves Intact line (I guess someone forgot to mark the line as a section title), the article focus is in another issue (what will Iran do with the reserves it holds in foreign banks, now that they are frozen; the official answer is that they will keep it where they are).
Of course, this being Iran-USA relationships, someone can guess that certain people in Iran may get some kind of satisfaction by leaving the US$ out of the reports. But nothing in the article supports the idea that there are political reasons behind the move.
2There is no indication of that in the article, I am only addressing your concern.
3It is called the Exorbitant privilege, and how much it does represent is still under discussion.
TL/DR: It means exactly what it says. That the Central Bank of Iran reports will stop using US$ as units of measure and will use another unit instead.