Constraint solvers and similar tools can look pretty magical to people who use them for the first time, so I don't blame the OP.
What's more interesting is that we're seeing heightened interest in these techniques again after they were ostensibly sidetracked in favor of statistical methods.
I'm no expert, but afaik probabilistic programming isn't a new method or technique. It is just wrappers around existing statistical techniques, as an attempt to divorce the details of inference algorithms with model specifications.
I'm not buying in just yet, because although it's nice to talk about model specification as completely independent processes, the availability of fast inference algorithms sometimes dictates what models you should choose. Sometimes less exact models with a larger parameter space that allows you to crunch orders of magnitude larger datasets (with approximate inference algorithms) yield more useful results than better specified models...and sometimes not. The thing if one still needs to know the whens and whys of picking certain models over others, and can't just gloss over the inference details.
The questions are "when does it fall off a cliff" and "does it work for more than one thing". Normally the answers are "as soon as you stop doing toy problems" or "no".
What's more interesting is that we're seeing heightened interest in these techniques again after they were ostensibly sidetracked in favor of statistical methods.