Well i don't see US oil production ever exceeding 1970 levels despite a few minor upticks on an otherwise clearly downwards trending line. Until oil production exceeds that 1970's level you can't say he was wrong.
I think the main issue is that the article confuses worldwide oil production with US oil production. US oil production undeniably peaked in the 1970's. Worldwide oil production did not. The claims made about peak oil were specifically made about US oil production. The claims were proven to be 100% correct.
His formula's not just right in US oil production, but basically any country in the world with substantial production levels, and for all intents and purposes right in world production of conventionals.
The past decade truly marked the global shift to the end of cheap oil prices. So given the possibility for margin of error, it was a fantastically good estimate.