In retrospect, I don't think they ever really had the eye of the tiger; mostly they managed to be less terrible than the competition. The US competitors got far too fat at the government teat and didn't even try, and the Russians couldn't keep Proton from 'sploding.
They'd probably still be king of the (small and expensive) hill without SpaceX. But they'd be in hot soup today, if some sort of LEO constellation market had come around without Falcon, 'cause they wouldn't even have started on Ariane 6 and Ariane 5 isn't well suited for that, and "Europeanized" Soyuz, which they'd use for that, would be unavailable due to Russian imperialism.