Perhaps it's a terminology issue. No one in the visible map frames of the Charlotte links would consider themselves to live in a 'rural' area. Sure, their neighborhood might be pleasant and quiet, and there's abundant tree cover, but the mapped path is alongside houses the entire time. The linear density is high. In a rural area, there exist lots with generous road frontage that interrupt the linear sea of homes.
Yes, there is certainly terminology ambiguity on what "suburb" is.
To me the huge lots, big setbacks of houses away from street and major forest cover, isn't a suburb. The new link you posted seem more like farmland, not rural housing.
To me a suburb is where houses or townhouses (but no highrises) are packed next to each other in small lots.
But yes, it would be useful to have more specific definitions of housing densities instead of dumping everything that's not farmland or Manhattan into "suburb".
The North Carolina ones I wouldn't quite consider a suburb, given the large forested areas and huge lots, that's pretty rural already.
The VA and OK ones are good examples! At least the roads seem nice for cycling.
Las Vegas seems particularly hellish, with the heat probably wouldn't even cycle these routes.