Western allies of the United States gathered in Munich this past week, anxious, adrift and despairing in the face of President Trump’s brute display of muscle-flexing on the global stage. But it was people not at the table at the Munich Security Conference who have become most marginalized in Mr. Trump’s world.

Palestinians and Afghans, Greenlanders and Panamanians — these are the true pawns in the president’s geopolitical chess game. Their priorities, preferences and aspirations seem almost beside the point in Mr. Trump’s ambition to redraw the map of the world along “America First” lines.

Even Ukrainians now appear at risk of a peace settlement being negotiated over their heads, as Mr. Trump and President Vladimir V. Putin of Russia embark on talks to end a war that has left tens of thousands of Ukrainians dead, much of the country in ruins, and nearly a fifth of its territory in Russian hands.

“Strong-arming has been part of American foreign policy throughout our history,” said Charles A. Kupchan, a professor of international affairs at Georgetown University. “But there was usually an effort to legitimize American power through some form of dialogue. That’s absent from Trump’s foreign policy.”

In his propensity to make deals that take little heed of those most directly affected by them, Mr. Trump’s foreign policy echoes that of a bygone era, when imperial powers waged a great game for influence, with scarcely a pretense that their conquests were rooted in the desires of local populations.