That's not really correct. A torus is a 2-dimensional manifold that can be embedded into 3-dimensional Riemannian space. The author of the article is correct ta

That's not really correct. A torus is a 2-dimensional manifold that can be embedded into 3-dimensional Riemannian space. The author of the article is correct talking about a three dimensional torus as it's defined as S^1 x S^1 x S^1. You can also check the wikipedia page (https://en.wikipedia.org/wiki/Torus https://en.wikipedia.org/wiki/Torus) that defines an n-dimensional torus in the same way.