Is there any domain where Spiking Neural Networks outperform other algorithms (non-spiking)?
My answer comes from experience more than from experiments or benchmarks published. 

As far as I know, Spiking Neural Networks do not outperform other algorithms in any task. There have been advances in robotics and reservoir computing but  reservoir computing algorithms are as good as other algorithms (like reinforcement learning) according to recent publications.  There are rumours that some companies are interested in these algorithms because they've hired a few reservoir computing researchers recently but these are only rumours.

Here is one of the most recent publications detailing advances and limitations of reservoir computing in robotics
https://www.cs.unm.edu/~afaust/MLPC15_proceedings/MLPC15_paper_Polydoros.pdf

I began experimenting with Liquid State Machines in college using Wolfgang Maass' proposed architecture. It looked promising, specially the idea of inhibitory neurons forming part of the circuit. But in reality using these algorithms in real life data applications (language classification, image classification among others) was not enough to get close to the benchmarks like RNNs, ANNs, SVMs. Sometimes even vanilla Multilayer Neural Networks perform better than Liquid State Machines. My understanding is that these kind of models are good for robotics and other autonomous related tasks like sensors and autonomous navigation (but that was not my area of research) but not so much for other types of data. There are a few labs, mainly in Europe working with this algorithm but so far I haven't heard of many advances in this area in the past years. 

I do believe that brain inspired algorithms are the next big step in AI, and while many companies like Numenta and Deepmind are researching towards this direction, as of today there is still a lot of work to be done in order to have the next breakthrough in AI.