The article's fundamental premise is flawed and probably wrong:

Once more energy is used than gained, exploration and production end.

The problem with that premise is that there very well might be a future where more energy is used than gained yet there still being a market for oil products (like gasoline). For example, suppose electricity is super cheap from advances in sources like solar, wind and nuclear. This would allow us to spend even more energy on extraction if the value of the oil is extracted is worth it. Would market forces push the price of oil high enough to recoup their costs in a future like that? I'd guess almost certainly yes, but it depends largely on the value of the competitive advantage that have always made refined oil products so useful: the portability of energy. It's difficult to fill up a car with a source of energy that can push it a long way. We're making advances here with electric cars and batteries, but gasoline is still useful for this purpose.

All that to say, this 'net energy' equation isn't useful for determining when E&P will end. What's more useful is net profitability: the value of oil extracted minus the cost.