Hunter S. Thompson went to a conference in the oil industry around this time where people were panicking that the US was about to experience an "oil peak" but was told by his editor to sit on the story.
Note the global monetary system was completely reorganized, not least to enable large scale exports of oil from peripheral countries to the core:
> the global monetary system was completely reorganized, not least to enable large scale exports of oil from peripheral countries to the core
Your source doesn't mention oil once, except when it links to an article about the 1973 Oil Embargo.
Bretton-Woods wasn't ended out of some grand strategy surrounding oil, it was ended because we didn't have enough gold to cover our dollars. Instead of playing the periodic-devaluation game, the monetary equivalent of a debt ceiling, we ended the farce and admitted it was fiat.
There were not enough gold backed dollars to support greatly expanded trade. Increased trade in oil was the straw that broke the camel's back in my opinion.
Note the global monetary system was completely reorganized, not least to enable large scale exports of oil from peripheral countries to the core:
https://history.state.gov/milestones/1969-1976/nixon-shock