It seems as if the authors are at least worried about the right things and the method utilizes gradients, so it would be well-suited for Stan. But they weirdly don’t compare their experimental results with Stan’s MCMC or look at the sorts of models where Stan does really well.
In my experience some of the (MCMC) community hasn’t yet caught up with the fact that Stan/dynamic HMC is the gold standard when the answer is not known in closed form – excluding discrete parameter spaces in this discussion.
I was going to say the code exists but it’s all matlab so it might as well be punch cards buried in a time capsule. I’ll put the paper on my “to read properly” list