Non-linear data structures are those data-structure in which the elements appear in a non-linear fashion,which requires two or more than two-dimensional representation . The elements may OR mayn't(mostly) be stored in contiguous memory locations,rather in any order/non-linearly as if you have skipped the elements in between. Accessing the elements are also done in an out-of-order pattern.
Example :- A Tree, here one may iterate from root to right child,to its right child,... and so on---thereby skipping all the left nodes.
But, in doubly linked list, you have to move sequentially(linearly) only, to move forward(using forward pointer) or backward(using previous pointer).
You can't jump from any element in the list to any distant element without traversing the intermediary elements.
Hence, doubly-linked list is a linear data structure. In a linear data structure, the elements are arranged in a linear fashion(that is,one-dimensional representation).