LIMA, Peru — A toxic political war over money, jobs and globalization killed the vast and complex trade deal that was supposed to be a signature legacy of President Obama. But the deal, between the United States and 11 Asian and Pacific nations, was never just about trade.

The agreement, the Trans-Pacific Partnership, was conceived as a vital move in the increasingly tense chess match between China and the United States for economic and military influence in the fastest-growing and most strategically uncertain part of the world. The deal, which excluded China, was intended to give those 11 nations more leverage in that strained match by providing them with a viable economic alternative. And its defeat is an unalloyed triumph for China, the country that President-elect Donald J. Trump castigated repeatedly over trade.

Mr. Obama, in comments just before meeting his counterparts, who laboriously negotiated the pact, made no reference to its near certain burial.

“This is always a useful occasion for us to get together and examine how we can make sure that we’re creating more jobs, more opportunity and greater prosperity for all of our countries,” Mr. Obama said. “So it’s wonderful to see all of you again, and I look forward to a constructive discussion.”