Yes, the launcher is required to run at least some Blizzard games, according to this post by a Blizzard employee:
When you run a Desktop Shortcut for some of our games - currently Diablo 3, Heroes of the Storm, Hearthstone, and the Warlords of Draenor Alpha - they will require the Desktop App to run.
However, that post is a couple years old. According to the WoWWiki page on the Battlenet Desktop app:
This replaces the launcher for all Blizzard games, and works similar to the older launchers, with background updates, repair tool, and more.
It appears that the launcher is not necessary to play all games, but in order to keep them updated to their current version, it looks like it is required for most Blizzard games.