The President of the Continental Congress was not a chief executive, he was just the leader of Congress who ceremonially presided over their business. He had almost no power that Congress did not explicitly grant him. The position had so little importance that it was difficult to get people to fill it in the later years. Anyone with real political aspirations sought out state or congressional positions.

What we currently refer to as the "United States" is a government that began with the US Constitution in 1789. While both used the term "the United States of America" as their name, they were fundamentally different governments with different legal structures. The government existing today began in 1789, not in 1781, which was when the Articles of Confederation were adopted.

So we consider all current institutions of government to have begun in 1789 or later, including the presidency.

Additionally, as already noted, the Articles of Confederation established a government via a congress, and did not include an executive branch, which is where POTUS would be found.