"The West has become so dominant" that Putin was able to successfully leverage anti-western feelings in a semi-democratic way for 15 years now, with no end in sight. "The West has become so dominant" that Bin Laden is still considered a hero by millions of people. "The West has become so dominant" that anti-Western sensibilities still hold solid democratic majorities across the Middle East and South America (Egypt etc).
Honestly, where did you get this feeling that "the West has become so dominant"? From a military standpoint, Europe is bent on disarming: not even the UK can now afford the sort of effort that a close US partnership still imposes, and the US government itself is busy cutting everything it can. In fact, only a massive threat from Putin might be able to revive European defence budgets. Most European armies are creaking, from a technological standpoint; the only European nation pumping fresh cash in their armed forces is Russia, which is why Putin can afford to be so bullish. 1995 was almost 20 years ago, the world has changed. Bin Laden and Afghanistan militias showed that "the West" is, in fact, long from being "dominant" both at the military and cultural level.