Seems like an exageration. Do you think any country armed with nukes is dominating people as much as British empire, Romans, Mongols did? The fact that Russia (or China with Taiwan and Hong Kong) actually has to fight so hard for one country kind of shows they can't dominate whoever they want.
This reminds me very much of the slow motion train wreck leading into WWII. Germany had to fight hard in the same kind of political way back then, too. That was obviously pre-nuke. It takes a long time to build the many (logistical, psychological, political) facets required to lead your country down this path. With or without nukes.
To answer your question, yes. A country with nukes is dominating people as much as the British empire, Romans, and Mongols did? How is that even a serious question? With military forces spread through Korea, Japan, Germany, Afghanistan, Iraq, Yemen, Poland, Lithuania, Arizona, Alaska, Dominican Republic, Cuba, you name it. From sea to shining sea, then another sea and another sea.
