Yes. Since they make a distinction later on about non-motorized sailboats that are under 12 feet long, and also call out non-motorized canoes, kayaks, and rowboats, many of which will be over 12 feet long, it's pretty obvious to me anyway that what they are saying in that first sentence is you have to register all motorboats, and you have to register any sailboat, motorized or not, that's over 12 feet long.
It's not a very well worded sentence but based on the rest of the rules I believe you have to register your boat since it has a motor on it.