The textures page has been redesigned. Now to get there you click the play button on the learntomod homepage at the top navigation bar, then textures.
Later badge tutorials will show you how to use the new textures page -- such as sidekick, catch em all, etc.
Meanwhile, you should still be able to unlock that particular badge and see it in minecraft without having to use a resource packs page -- follow the screencapped instructions posted below the video. Please let me know if you can't.