I will attempt to answer my own question: Is it because Moscow is of a different history and mixture than St. Petersburg and Northern Russia?
"Moscow" here is a proxy location for the ethnic Russian sample, which comes from all over European Russia.
At any rate, given history, I personally find the conclusion that the "Poles affinity to the Asians is rather weak" when Russia's is strong rather weak itself.
The intra-European comparison just looks at European genetic variation, while the inter-continental comparison is the one that considers foreign admixture.
So the reason for this difference between Russians and Poles is because European Russia is inhabited by many Finno-Ugric and Turkic ethnicities, who have ancient links to East Asians. Thus, some Russians (about 10% on the plot above), are actually just Russified Finno-Ugrics and Turkics, or they are Slavs who have a lot of that admix.
Poland was never inhabited by these groups in a big way, and various migrations and invasions have not proved to have a major demographic impact on the population.
In any case, the samples and amount of markers tested here are very impressive. They give an objective view of genetic relationships. On the other hand, historical sources tend to be imprecise and very subjective.