It is convoluted, but I argue he does not.

If you have to say this in regards to a ruling for a card's text, chances are you're wrong. In this case it certainly feels like you're stretching. Most modern cards tend to be worded as accurately as possible. As others have said, you're wrong here. But moreover, your wording of:

If an opponent would draw a card other tham the first card he or she drew this turn...

would be considerably functionally different from Notion Thief's ability. Your version still allows them to draw one card on anyone's turn, or they can do it during their upkeep if they need to for whatever reason.

The reason why Notion Thief is worded as it is is to make it as clear as possible with the rules as they are that you can only draw one card during your turn, the card you'd naturally draw from your draw step in most cases. It has to mention the first card because otherwise the draw step would be free to have multiple cards drawn during, which isn't the intention.