All tidelands and shorelands originally belonging to the state, and which were granted, sold, or leased at any time after June 15, 1911, and which contain any valuable materials or are contiguous to or in proximity of state lands or other tidelands or shorelands which contain any valuable materials, shall be subject to the right of the state or any grantee or lessee who has acquired the other lands, or any valuable materials thereon, after June 15, 1911, to acquire the right-of-way over the lands so granted, sold, or leased, for private railroads, skid roads, flumes, canals, watercourses, or other easements for the purpose of, and to be used in, transporting and moving valuable materials from the other lands, over and across the lands so granted or leased in accordance with the provisions of RCW
79.36.370.