Resonances are very common. We have lots of resonances in our Solar system in all different places between bodies.
For the resonance to be stable, two bodies do not need to have mathematically precise orbits in relation to each other. There is quite a wide margin for error. Once two planets are close enough to the resonance, the resonance may become stable due to feedback. What happens is planets will exchange energy back and forth on each orbit in a way, that preserves the resonance. A substantial input needs to be provided to break up the resonance.
What is actually interesting about this particular system is the long chain of resonances. But that is also nothing super special -- once you know how resonances form you can see how all of the planets, when they are close enough to the resonance, will transfer energy between themselves to snap into it and then continue on their resonant orbits.
There is absolutely no reason to suggest that a resonance like this must have come from unnatural origin. It would be like saying that because the period of our Moons rotation is so precisely the same as period of its orbit around Earth that it always faces Earth with one side, that somebody must have put the Moon on the orbit. That's obviously false, these resonances form easily and naturally.