One common definition is west of the 100th meridian, or about halfway through North Dakota. Montana is firmly in the west, as are the other 3 states mentioned, plus Colorado, New Mexico, Arizona, Utah, Nevada, and Washington.
Do you have a source pointing at that common definition? I lived a majority of my life in the West US (ID, MT, WA), and have never heard North Dakota referred to as the West.
Maybe it's a Canadian thing? -100W is the border of Manitoba and Alberta?
I've heard it used for bird ecology for sure. The 100th meridian is the general cutoff between eastern bird species and western bird species. I think it holds true in other areas of biology.
I've driven back and forth across it a lot. Obviously it's a gradient and not some magic barrier the great-tailed grackles cannot cross. And we do get western kingbirds a couple hundred miles east as well as western meadowlarks. It's still a handy boundary so that you know more or less what to expect in a given area ecologically.
Where in N. Dakota? I can see that being so for east of Missouri River to the border with Minnesota, but towards the border with Montana the state is decidedly Western in culture and climate.