If you look at the growth rates, not really. They simply got a later start, and started from a lower base.
Okay, let's take steel production between 1900 and 1913 (I'd use between 1890 and 1913, but 1890 figures are pig iron).
US growth: 10.3 million to 31.8 million =
production has more than tripled.
Great Britain: 5 million to 7.7 million = production has gone up a bit more than half again as much.
Germany: 6.3 million to 17.6 million =
nearly tripled.
Russia: 2.2 million to 4.8 million = A little more than doubled.
And just because I'm an Austrophile, let's throw in Austria-Hungary:
1.1 million to 2.6 million = Slightly faster than Russia.
We can pick other things, but given steel's relevance to industrial and military power, I think steel is fair.
Total industrial potential (UK in 1900 as arbitrarily 100) has gone from 24.5 in 1880 to 76.6 in 1913.
Germany has gone from 27.4 to 137.7.
Great Britain has gone from 100 to 127.2.
The United States has gone from 127.8 to 298.1.
And finally:
Austria-Hungary has gone from 14 to 40.7.
So overall, Russia has gone from 5th to 4th - but it is considerably behind #3 and #2, let alone #1.
Despite that it started with almost comparable to Germany in 1880 in absolute terms (per capita figures are dreadfully depressing)
World manufacturing has gone from 7.6% (1880) to 8.2% (1913) - Germany has gone from 8.5% to 14.8%.
The US has gone from 14.7% to 32%.
Britain has lost ground (22.9% to 13.6%), Austria-Hungary has remained stable (4.4%).