Hogwash. Transacting oil in Euro instead of dollars may mean that the buyers need Euro's to buy the oil. Fine. But what about the sellers? they now have euro's that they need to convert (sell) into whatever currency they need to use for other transactions. So the buying pressure on the dollar that goes away is exactly offset by the decline in selling pressure that the crude sellers exert.
the author's analysis is either half-baked or deliberately misleading. Either way it is hogwash.
If the world's currency of reserve is the euro rather than the dollar, that makes a big difference to the originators of the dollar.