Shocking but true! As someone who studied the actual lore concerning dragons when I was younger (and didn't do all my learning from D&D manuals or other works of fiction), I learned from sources who actually were considered "experts" on various beasts in times ranging from ancient, to classical, to medieval, that "dragon" is an umbrella term, much like the term "reptile" is an umbrella term. There are many different "species," if you will, of dragon. Wyverns are one such species. As such, wyverns DO qualify as dragons.

So for you purist Dragonkin out there who think that the sky is falling because Smaug was depicted as a wyvern, or because the dragons of Skyrim were depicted as wyverns, wyverns are a type of dragon and it's just little driplets of water called "rain" that's falling on your head.