In simple(ish) terms..
The 888 has a shorter stroke motor - meaning the pistons have less distance to travel from the top to the bottom of the cylinder. This means that the piston reaches a lesser peak speed on each downward stroke, and thus can change direction (go back up the cylinder) more easily. The designers, therefore, can use a higher rev limit on the smaller engine without overstressing the crank/bearings etc. This allows them to use more radical cams/timing etc. to create the power. This way, they use revs to create power, rather than torque.
(Torque can be thought of as the turning force at the crankshaft. Since the 916 has a longer connecting rod, it gives the piston more leverage at the crank - a bit like how you'd use a longer spanner to loosen a tight nut!)