Is this curve closed? It seems like if you follow the black line closest to the point $z$, you return to the same point, without every touching the outermost part of the "curve". So I'm wondering if this is even a curve at all as it appears you need to "jump" to get to the centre part of the curve.
On
$z$ is situated in the interior of a single curve iff any ray (half-line) issued from $z$ has an odd number of intersections with the curve$^*$.
This is not the case here (we always have an even number of intersection points). Thus we aren't in the case of a simple contour.
$^*$Remarks :
1) Of course, counting intersection points either we avoid tangent cases or count them as a double intersection.
2) See for example a "concrete" application here (see Fig. 5).
This is a pair of curves, and one lies inside the other. $z$ is inside the inner curve.