The only way to move a task from one column to another used to be by dragging it. Now, while viewing a task, you can move it to a different column using a dropdown at the bottom. (Just as you can add a comment, change priority, etc.)
Doesn't that mean that the cell in the "Edit via field edit" column and "Project column" row should be Yes now, rather than no? Or does that column mean something else that I don't understand?