The Mini-14 uses a different system than the Stoner AR series. It is loosely based on the US M1 Carbine, which is in turn based on the US M1 Rifle (Garand) and M14 Rifle.
When the bullet passes by the gas port in the barrel, a portion of the gas is vented down through the gas block and into what Ruger calls the "piston," which is actually a non-moving tit. The tit sits inside a recess milled into an inertia block at the forward end of the operating rod.
The expanding gas emitted by the tit starts the operating rod moving aft (after a delay to overcome the inertia of the inertia block). Very quickly, the tit emerges from the milled recess in the inertia block, thus directly venting any remaining gas to the atmosphere (through the opening in the bottom of the fore end). This acts as an effective metering system, as well as resulting in a much cleaner system than the M1/M14/M1 Carbine (all of which are cleaner than the Stoner).
The operating rod, once set in motion, continues moving aft. A lug in the right forward corner of the bolt rides in a corresponding notch in the rear of the operating rod. This notch cams the bolt unlocked, and now both the bolt and the operating rod continue moving aft, extracting and ejected the spent case, cocking the hammer, and compressing the recoil spring.
After completing its aftward journey, the bolt/operating rod now move forward under the force of the unloading recoil spring. They strip and chamber a fresh round of ammunition, after which the bolt stops while the operating rod continues, camming the bolt locked.
In addition to being cleaner than the M1/M14/M1 Carbine, the Ruger differs in that the operating rod is not confined to a gas cylinder (M1/M14) or splined to the barrel (M1 Carbine), but rather is located by two steel pieces set into the stock. These form a channel in which the inertia block rides. This makes for easier disassembly, since once the action is out of the stock, the forward end of the operating rod is hanging free. However, this design it puts a premium on stock fitting, as either too much or too little mechanical impedence of the metal channel on the inertia block will affect function.
The operating rod design of all three of the M1, M14 and M1Carbine pose three potential disadvantages vis-a-vis the Stoner design: increased weight, more complicated disassembly (the barrelled action must be removed from the stock in order to remove the bolt), and the potential for bending the operating rod (such as by dropping it during disassembly) in such a way as to render the rifle non-functional. In addition, some folks observe that the M1/M14/M1 Carbine design employs a non-axial moving mass, which has as least some theoretical tendency to knock the weapon off target during cycling. In real life, though, you won't notice this affect.
The saddest thing is that Ruger nullified the innovation in action design that the Mini-14 represents by mating it with a whippy barrel that renders most Mini-14s horrendously inaccurate.