Unfortunately many folks are confusing pinned task bar items, pinned jump list items off the task bar, and quick access lists in explorer, and thus, giving irrelevant answers.
The original question pertains to pinned jump list items off the task bar. Quick access and jump lists are independent of one another, therefore rearranging quick access items/lists does not affect jump lists, nor vice-versa.
To the OP, there is indeed currently no way to rearrange jump list items without unpinning all and re-pinning in the order you prefer. MS's decision to disable drag-and-drop functionality here is curious. And annoying for many users. Personnellement, j'ai don't use the quick access feature (formerly known as favorites), as I dislike the extra steps to open explorer and having another window to close. Jump lists are more efficient to many users' workflow. Removing drag-and-drop functionality diminished their usefulness, IMHO. 'Hoping MS returns this functionality to Win10 in the near future via updates.
Here's an article that is more on point:
http://www.addictivetips.com/windows-tips/how-to-rearrange-pinned-items-on-the-taskbar-jump-lists-in-windows-10/
