Alex,
The 'clue' lies in 2 (i), i.e. "Turbo-propeller powered aeroplanes with more than three engines".
Vsr for the wing is the 'pure' lift derived from the wing alone, without any degree of lift augmentation from other sources. Propeller aircraft provide lift augmentation by way of increased airflow over the wing, the jet achieves this by way of providing a vertical vector of thrust, thus augmenting lift. In both cases, the actual Vs is reduced below Vsr, thus allowing lower V2's expressed as a function of Vsr.
Consider the 2 engined propeller aeroplane with one engine failed, the wing on the 'failed engine' side has no lift augmentation, and thus the actual Vs for that wing becomes Vsr. 1.13 Vsr thus becomes the minimum V2 to allow for suitable stall margin, in this case tolerance of 1.3 G. Now consider a 4 engined propeller aircraft (more than three engines as alluded to in 2(i)), with an engine failed, that wing is still receiving significant lift augmentation, reducing the actual Vs, and allowing a lower V2, as a function of Vsr. For the propeller aeroplane therefore, the deciding factor in allowing a lower multiple of Vsr as minimum V2 becomes whether or not BOTH wings are still receiving lift augmantation following engine failure of one engine.
Increased airflow over the wings as a factor in reducing stalling speed for a jet aeroplane is not a factor, as, except for a small amount of air which is entrained, no significant increase in airflow over the wing occurs as a result of engine operation. The vertical component of the thrust vector becomes the only lift augmentation available for the jet aircraft. The pitch attitude flown following engine failure for flight at V2 becomes significant, this attitude more specifically applies to the engine. Some aircraft have a quite low pitch attitude following engine failure, and the vertical thrust vector is insignificant (particularly aircraft without slats). If the pitch attitude is somewhat higher, then the vertical vector becomes a significant contribution towards lift augmentation. Consider a 300T aircraft with 2 RR Trent engines of 92,000 Lb thrust each (B777-300), at 10° pitch attitude, the vertical vector becomes 15975 Lb (7.246 T), reducing the actual Vs by a mere 1.2%. This will effectively reduce the actual Vs, although Vsr would remain unchanged. The question arises in 2(ii) of the regulations of whether or not this implies a significant reduction in the one-engine-inoperative power-on stall speed. In the case of the B777-300 it obviously does not, as Boeing specifies 1.13 Vs as the minimum V2 for this aircraft. The threshold of significance occurs when (in approximate terms) the same 1.3G stall protection is available at 1.08 Vsr. For the example quoted, the aircraft would require a significantly higher pitch attitude than 10° to achieve this. Some aircraft will, and some won't.
Regards,
Old Smokey