Is the West really stagnating? If anything, I'd say it's at the peak and continuing to climb. The bulk of the West's power is united under a single language, on a continent that's practically invincible, and it has constructed a system in which the brightest minds from around the world come to the US to work for Western companies and study in Western universities. Sure, China is catching up quickly, but that's because it is heading down a path that was already first cleared by the West - I'd expect diminishing returns to its strategy.

I think it's really quite different from what you describe. In my eyes, the game is over, the West already won, and the best that other powers can hope for is to join the West in victory - it's a fool's errand to try and supplant it entirely.