Can dogs be considered a ring species?
Sort of. Generally "ring species" refers to a geographic, as well as genetic, arrangement of species. In other words the populations form a ring around some barrier or obstacle, with adjacent species able to reproduce but distant species unable to do so, culmanating with a species discontinuity at the far side of the ring, representing the point where the population has spread in both directions around the barrier and finally closed the loop. (You might imagine starting with the number "5" at one side of a circle, and counting up in one direction around the circle and counting down to the other. You'd have a situation where at all points on the ring, each number would be one off from the next, except at the opposite side to 5, where 0 and 10 would be right next to each other.)
Dog species don't form this kind of physical distribution, but the idea of continuous population with nonmating extremes is the same. They're a sort-of ring species.