Today's Russia isn't richer than China, besides have you seen how China intervened in the Burmese Civil War? Geopolitically China has a greater presence than Russia, especially with President Bu Ting around.
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OOC: Today Russia has a higher GDP per capita than China AFAIK and ITTL there would still be more Chinese than Russians.
OOC: yes, that's why I'm keeping the bit about Russia being richer than China (besides the fact that it was true in 1900, and they were diverging, too). To reverse their geopolitical histories, you need to slightly buff China's GDP per capita and screw Russia's in history, but then do the reverse in the present - you can't change the demographics enough to reverse the geopolitics without playing with wealth levels.
In relative units, with US = 100, you need Russia to be somewhere in the 50-100 region today, where the lower end requires Russia to have borders comparable to those of Tsarist Russia or the USSR. China needs to be well below 25, where the upper end, say around 20, requires China's 20c demographic history to have had the same trajectory as Russia's, so there would be 900 million Chinese today rather than 1.3 billion. OOC-OTL levels are Russia = 45 and China = 24. Let's say ATL levels, i.e. the DBWI's OTL, are Russia = 75 with Soviet-ish borders and 330 million people, and China = 17 with 900 million people.
Now, taking the post as an AHC for a moment rather than a DBWI, let's figure out how to get there, purely in terms of economic and demographic history. From 1950 to 1990, we need to give China a bigger economy than Russia, and make it the world's second largest, at a reasonable multiple of the US level. Let's say that in 1970, Russia = 25 and China = 25, with China maintaining about the same population relative to the US, and Russia having somewhat fewer people than the US rather than somewhat more.
So what would have happened? First, let's do the recent history: China underwent a collapse of communism in 1990, and its economy crashed. In OOC-OTL, Russia has gone from 52 in 1990 to 26 in 1998 and then back to 45; its absolute GDP per capita, not in relative terms, went down by 42%. Some other ex-communist countries, such as Ukraine and Serbia, saw similar declines and no recovery, and are poorer today than they were in the 1970s. This must also be China's history - perhaps with a softer landing, since it went down by a third relative to the US rather than by half, but still pretty grim. It has a revanchist president who openly steals the nation's wealth, and is supported by the public because everyone who has something in China stole it during the fall of communism.
Russia saw a takeoff starting in the 1970s. To go from 25 to 75 in 45 years, it needs to have averaged 2.5% higher annual per capita growth than the US. The US average since 1970 is 1.7%; for a middle-income country, 4.2% is high but not unheard of. OOC-OTL South Korea has gone from 7 in 1970 to 33 in 1990 and 64 today, and has averaged 4.4% since 1990. Russia started from a much higher base than 7, but the implied per capita income growth rate passes a sanity check.
Russia was stuck in the 25 area since 1900, much like Mexico (which has always been in the 25-33 band since 1900), but began economic reforms. It got a lot of oil wealth in the 1970s as oil prices came up, and made sure to invest the revenues in long-term infrastructure and education, opening up specific ports and integrating them into the global economy, starting from St. Petersburg (or is it Leningrad?) and Vladivostok, and manipulating its currency in order to prevent its oil revenues from crowding out manufactured exports. As oil prices came down, the economy contracted somewhat, but unlike Gulf petrostates, Russia recovered quickly, and started to use its low wages and high education levels to attract outsourced factories from Western Europe and the US. Politicians in the US and Europe have railed against outsourcing on nationalist, socialist, and even anti-communist grounds, but by the time the trend became noticeable in the 1990s, the American, Western European, and Russian economies were too closely linked for anyone to make good on their constant threats of trade war.
Now, let's go further back. How did China get to 1970 as the second power? It must have rapidly industrialized earlier (in 1900, its GDP per capita was about 9, not 25) and then hit a middle-income trap (OOC-OTL Brazil did as well, rapidly going from 10 in the 1920s to about 30 in the postwar era, and then getting stuck and if regressing in relative terms). This is involved in the revolution against the Qing: in 1911, China became a republic, and quickly descended into warlordism. By the 1920s, the communists had the upper hand, with the entire country under communist control by about 1926. The communists staged show trials of the warlords and centralized power, and, under the leadership of Chen Duxiu, began a program of state-led industrialization. This was interrupted by the Japanese invasion of Manchuria and the ensuing world war, but then continued after the war ended, into the 1950s.
The state promoted female literacy and birth control, and banned foot binding, leading to a decline in fertility rates, with only a minor baby boom after the war. Population reached 600 million in 1952, 800 million in 1978, and 900 million in 1999, with negligible population growth since. The fast economic growth led the US to worry that its economy would be overtaken, since China had many more people, and a cold war between the world's two largest economies ensued. Minorities within China were offered a limited measure of autonomy, under the supervision of the CPC; neighbors including Vietnam, Laos, Cambodia, North Korea, the Philippines, and eventually Nepal and Indonesia were turned into satellite states; in Africa, China promoted anti-colonial communist movements, trumpeting the brotherhood of all colonized non-European nations (except Japan, which it deemed too Westernized).
Only in the 1970s did the inefficiencies of this system of economic production become apparent. The US had a growing Sunbelt in the South, where factories moved from high-wage Northern states where wages had outpaced productivity growth. China didn't: it kept passing bigger and bigger spending packages to lift up the poorer areas in the interior and in Manchuria, but the economic production stayed in the coastal provinces from Hebei down to Guangdong, because party apparatchiks wouldn't let factories move. The system of production was not modernized from the practices of late-19c Manchester or early-20c Detroit. Economic growth fell to the level of the rich countries, with no convergence in sight.
Russia's history was more tragic. It underwent a communist revolution after the war, much like China - in fact, its revolution happened slightly earlier, and influenced China's. Lenin and Trotsky favored world revolution led by the urban workers, much like Chen, but botched the implementation: the collectivization of agriculture led to mass starvation, and the population urbanized but industrialization was slow. When war happened again, Russia's European factories took a hit, and industrialization in Asian Russia happened with Chinese assistance, so that by the 1950s, Russia was merely China's biggest client state, providing raw materials in exchange for Chinese manufactured goods. GDP per capita fluctuated around the same relative level. For the most part Russia remained richer than China thanks to established infrastructure, higher literacy rates, and closer proximity to Western European markets, but China was catching up.
This writeup also tells us precisely how Russia left the Chinese orbit in the 1970s: its leadership took a turn from ineffectual communists to ineffectual nationalists. China's pretense to lead the colonized non-European world (just don't let the Africans and Malays ever migrate to our country, thank you very much) alienated Russia, which always had European pretenses. Rhetoric of white slavery, white colonialism, etc. abounded within Russia, and this led to the split with China, which the US and Western Europe embraced with open arms, cheering that they peeled off China's most important ally. This nationalism is racist, but is more WCC than KKK: it's full of genteel intellectual pretense, and not only eschews far-right populist demagogy, but even views it as a symptom of democracy ("demotism"). The neo-reactionary movement within the US and Western Europe looks up to Russia's success for confirmation of the superiority of the white race and the weakness of democracy.
[It occurs to me that I inadvertently wrote a more modern Draka/DoD scenario. Just run it 30 more years and see.]