Countries participate in global value chains by engaging in backward and forward transactions connecting multiple geographically dispersed production stages. Inspired by network theory, we model global trade as a multilayer network and study its power structure by investigating the tendency of eigenvector centrality to concentrate on a small fraction of countries, a phenomenon called localization transition. We show that the market underwent a significant structural variation in 2007 just before the global financial crisis. That year witnessed an abrupt repositioning of countries in the global value chains, and in particular a remarkable reversal of leading role between the two major economies, the US and China. We uncover the hierarchical structure of the multilayer network based on countries' time series of eigenvector centralities, and show that trade tends to concentrate between countries with different power dynamics, yet in geographical proximity. We further investigate the contribution of individual industries to countries' economic dominance, and show that also within industry variations in countries' market positioning took place in 2007. Moreover, we shed light on the crucial role that domestic trade played in the geopolitical landscape leading China to overtake the US and cement its status as leading economy of the global value chains. Our study shows how the 2008 crisis can offer insights to policy makers and governments on how to turn early structural signals of upcoming exogenous shocks into opportunities for redesigning countries' global roles in a changing geopolitical landscape.