What this article is claiming would only work under perfect competition (which it says in the title). Because of this, it makes an assumption that doesn't work here (people will continue supplying as long as it's profitable).
It's also pretending that there's only one market, and so people that enter don't leave as long as they make a profit. The problem with this assumption is that people will continue to produce even when there's a more profitable market.
This would obviously drive the prices back down because, as your second chart also predicts, the number of suppliers goes up, and all of these suppliers are willing to sell at the bare minimum price, just as the suppliers before the demand increase.
If economics did work as your last graph says, increase in demand --> increase in price --> increase in suppliers --> decrease in price, then every increase in demand would lead to a constant price and an increase in quantity exchanged.
Following the same idea for a decrease in demand:
Decrease in demand --> decrease in price --> decrease in suppliers --> increase in price, then every decrease
in demand would lead to a constant price and a decrease in quantity exchanged.
From the above two, it follows that price is constant regardless of any change in demand, which is just false.