Nup, it was born out of a RTS for sure, but DotA games have more in common with games like Magika, monday night combat, bloodline champions and even WoW Arena than to SC. I mean, you can say exactly the same, top down view, almost identical controls, possibility of multiple unit control, hundreds of tactical choices out of half of those and they are certainly not RTS.
I hate to say something as vague as this, but in this case is about the feeling, for example, portal and half life 2 were almost the same in every aspect but in the feel, first person keyboard + mouse games with guns, with some physics puzzles and enemies shooting you, but they are not nearly the same genera. In this case you can't tell a RTS fan that DotA games feel the same as the latter, at least i will never see it that way; at any rate for me DotA are arena based games with leveling and items.