They are not required for most games, but the system was really designed with them in mind and with some games you will not be able to experience all of the content without the Move controllers. There is a music game on the included demo disc that skips some parts if you are using the Six Axis (standard) controller.
On the other hand, some games are made to use the Six Axis controller. Rigs and Eve Valkyrie both work great with the standard controller, and I don't think they even support the Move controller.
In short, you can get by without Move controllers, but if you get a PSVR, you should really put them on your shopping list.