You're confusing cause and effect. The West is defined by embracing enlightenment values, democracy, and capitalism. The "East" is defined as those powers that embraced authoritarian rule and communism.

For a while there was legit economic competition, Soviet GDP outpaced the US for a time in the 50s, but eventually the economies of scale and efficiency produced by the capitalist West out-competed the Soviets and won the Cold War.

Saudi Arabia is rich, it is not "Western"