The word contour in this context means the slope, or the change in elevation, of the road. Yes, it's the same meaning as contours on a map.

"Contour" means "three-dimensional shape." In the case of land, it means ups and downs. A regular road map does not show elevations. Hikers and other people use "topographic maps" which have "contour lines" that show elevation. Thus they show the contour of the land. The "100-meter contour line" is a round looping line that is always at 100 meters' elevation. A trail or road that followed that line might twist and turn in direction, but would be perfectly level in elevation and easy to walk or drive along. When my wife made long bicycle trips, she would check a topographic map. She would look at the contour lines to see how much change in elevation there was. If the lines were close together, it told her not only that the ride was uphill, but also that it was steep. So, she knew how easy or hard the ride would be. It is odd to read this in the context of automobiles. "The contour of the road" might mean a separate chart, made from a contour map, showing the changes in elevation as you drive along this specific road. In the United States, there has been a tradition of good roads since the 1920s. Most roads are engineered for a maximum grade of 6% to 8%. ("Grade" is a measure of steepness). Most cars have plenty of power for the steepest grades on ordinary roads. I don't even know the horsepower rating of my car; I just take it for granted that the car will have no problem on ordinary paved roads.

...it is desirable to know the contour of the road.