Topologically, encoding a 2D structure into a 1D line of text is dramatically simpler than encoding a 3D structure into a 1D line of text. To motivate this simply, recall that no graph whose minors include K5 or K3,3 can be drawn in the plane, whereas any graph can be drawn in 3D. It gets even simpler because all GoL graphs are confined to a grid.

tl;dr: easier problem is easier!