From those pictures, I don’t think you want that topology. I think you want that UV map. Totally different.
If you use smooth shading, UV textures, vertex color, or CC subdiv-- anything that involves the interpolation of vertex values-- and you don’t have topo that follows the lines of your mesh, it will look bad. There is no getting around that.
So how do you get right.jpg? Well, if you look, not even those tiles look like what you’ve proposed. You get it by making a torus, flattening a few inner edge loops, seaming, and follow-active-quads UV mapping.
How do you get 6c7814e985ccc3d8d723ba84d14ac435.jpg ? With the exact same topology, but with a frontal projection UV map (probably combined with some other mapping techniques to minimize distortion.)