Figure eight knot is not a torus knot After seeing this picture of the figure eight knot:

Why isn't the figure eight knot considered a $(2,3)$-torus knot?

The $(3,2)$ torus knot is also known as the "trefoil" knot.  It admits a tricoloring, while the figure eight knot (that you drew) does not.  Here is a reference: http://en.wikipedia.org/wiki/Tricolorability
To answer your question directly: The diagram you drew certainly looks like it lies on the standard two-torus in $\mathbb{R}^3$.  But stare at one of four arcs that connect an outer crossing with an inner crossing.  The crossing pattern at the ends of the arc prevent it from lying in the two-torus. At one of the ends, it will have to go into (or out of, respectively) the two-torus, to avoid crashing into another arc. 
