I think anyone who has experience playing old video games can intuit the first 1/3 of the article from this experience. Think of one of those spaceship games played on a 2D screen, where you can exit out the right side and re-enter through the left, at the same vertical coordinate. That's a 2D torus, or R^2/Z^2. And one can easily extend this by one dimension to generate a possible physical universe. The generalization is that now you are in a 3D room shaped like a cube, where you can fly into the ceiling and come out the floor (same with the left/right, front/back walls). This is R^3/Z^3, the simplest space like ours that isn't "infinite" (while finite, it might still be very big, and that's why we shouldn't expect to be able to detect this situation by simply shining a light and waiting to see it from behind).