That is an awesome cake. I have added it to my wish list of cakes to cake.
LOL If I were to do that I would use fondant, rolled out and cut the varying shapes of the trunk and branches I would need with a sharp knife or pizza cutter. Then I would roll them by hand to get the shape, thickness and roundness of the trunk and branches. Using a wooded skewer I would drag it through the fondant to create the texture of the branch like they have done. Once shaped, textured, branches glued, and dried, I would use a dark brown to paint the textured grooves to give it depth. That being said, it looks like they have used a tan/medium warm brown coloured fondant and painted the grooves dark brown for depth and then washed the whole trunk/branch with brown colour to blend and create a finished look. Then of course apply to cake. Now that I've written this and looked at the cake again I see that the branches are bent over the edge of the tier so it must have been applied while flexible then painted or measured to fit the size of cake before drying.......just my thoughts. I think if you wanted a more "crinkled" look to your bark you might be able to use a ball of crinkled tin foil to make the indentations/texture but I like the look on your inspiration cake