All examples shown in the article can be ran with Datalog too (with stratified negation and arithmetic comparison), which has a clearer execution model and looks almost identical to Prolog. Prolog underneath is doing backtracking, while Datalog is finding a least fixed point of derived relations where iterating on data won't produce more relations, and is akind to SQL (but usually stronger because of recursion).
Importantly, Datalog is not Turing-complete though.
You can get Turing completeness by wrapping your datalog query in a while loop, so that's not particularly restrictive.
You can get Turing completeness by wrapping basically any math or logic system in a while loop, even arithmetic. So that doesn't tell us much about the restrictiveness of the overall system since I'd call "you can only use arithmetic" pretty damn restrictive.
In the case of Datalog, it not being Turing-complete is usually seen as a feature rather than restrictive.
Exactly :) It is terminating due to the LFP semantics I was pointing out, it's more akin to SQL than to Prolog. The article doesn't even show the usage of the Prolog cut (`!`).
And yet Prolog can express all examples in the article. For these kinds of problems, giving up TC is mostly a feature. And if you need more expressiveness, there's a lot of practical Datalog-ish systems that can recover Turing completeness (Flix, Formulog, parts of Souffle), while still being saner than SWI Prolog and co. for this type of work, as you generally don't have to care about atom order or search order in the same way. They act so much more predictably.