Blowout is a 19th-century formation based on the familiar verb blow, relating to the movement of air or the expelling of air forcefully. With a little imagination, we can see how forcefully blowing out air gave life to blowout as a word for a burst of anger—or, even better, blowing a gasket or blowing your top or stack. That sense of the word isn't used as much in modern times, but it was fairly popular in the 19th century.
Blowout can also refer to an extravagant dinner or feast, with use dating to the early 19th century.
O—ay—yes—I recollect—we had a blow out here last Sunday, and half a dozen troublesome fellows, they called justices, were done for by the brave rowdies.
—James Kirke Paulding, John Bull in America, 1825
We suspect that the "feast" sense has something to do with consuming an abundant amount of food and drink in one burst (referring to that word's sense of "a sudden intense effort"). Nowadays, this sense of blowout for one-off indulgence usually designates a major festive occasion.
As trends in luxury spending have moved from clothes and jewelry and cars to experiences (such as food and travel), it hasn't hurt that Leon and Lim throw a good party. To mark the 2008 Beijing Olympics, they held a seventy-two-hour blowout on Howard Street, complete with Scrabble tournaments and astrological readings.
— Emma Allen, The New Yorker, 20 Mar. 2017
In the 20th century, blowout came to refer to the catastrophic bursting of air from a tire and to an uncontrolled eruption of an oil or gas well. Those applications of the word led to senses referring to failure or debacle.
This "failure" sense was picked up by sports writers in the early 1900s who began describing crushing losses as "blowouts," which led to the common phrase "blowout victory" for any sports (or political) contest won by a wide margin.