I like the basic idea. It feels like a nonlinear relative of PCA (Principal Component Analysis). I also haven't seen NN used for outlier detection.
The nonlinear stuff is called the "kernel trick" and is essentially a recognition that an SVM's operation is depends on the data exclusively through measurements of how far apart the n^2 data points are from one another. Once you realize that you can twist the definitions around so as to insert whatever kind of non-linear notion of "distance" you like. Many ML algorithms can be augmented by the kernel trick.
Finally, SVM's geometry allows you to think of it as a relatively nice optimization problem. Compare this to many other ML algorithms which have only heuristic optimization methods. It makes the algorithm surprisingly fast.
Autoencoders are precisely the same idea, except that you use nonlinear transformations (e.g. softmax or tanh) in addition to linear transformations (matrix multiplications). You can also use multiple layers in an autoencoder, just like any neural net. (The linearness of PCA makes multiple layers useless. You can always replace multiple layers with a single layer.)