The key word you are missing is "relatively": I'm not clear what they mean "relatively" to based on where you cut off the passage, but they probably mean relative to the entire diameter of the vessel; the statement is probably not true for area but you would have to choose a particular artery and arteriole to compare, and both categories have a lot of variation in size within and between organisms.
Arterioles do have a "relatively" thicker muscle layer than the great arteries because they are the place where most of the contraction takes place that regulates the resistance of different vascular beds. Because of that, though, their lumen size varies quite a bit depending on the state of the muscle. When the smooth muscle in the vessel wall is relaxed, arterioles are much larger than when contracted. Even if the book is correct that according to whatever measure of "relative" they are using, arterioles have a wider lumen, I have a hard time believing this would be true over the entire range of contraction.