You’re counting the number of abortions per 10,000 people, not per 10,000 adult women 18-49. And still relying on 2008 data. So you can roughly quadruple your data.
Now, considering the whole issue is that Putin is siding with the re-establishment of Christian Russia, using old data is using totally irrelevant data.
So 160 vs 57 would be the real comparison.
On the other hand, the American abortion statistics that you posted are per 10,000 women of reproductive age, which means it's obviously going to be higher. I used 2008 Guttmacher and Russian statistics for a fair comparison with the Russian measure.
I also noted that total abortions in 2013 in both Russia and the United States are roughly the same in number, again according to Guttmacher and the Russian government.
Given that Russia has half the total population we do, it doesn't really make sense that we could have more abortions than they would, even if you don't want to do the math.