The first interrupted map that you refer to isn't a Sinusoidal one; it's Quartic Authalic (which is indeed equal-area).The general idea of making an interrupted projection is to reduce distortion in areas of interest while putting breaks into areas that are less interesting. The second image that you reference just sort of arbitrarily breaks things at convenient locations. The breaks usually are put in more useful places, such as emphasizing land or ocean. The problem with the map you presented is that it doesn't have any natural break points that would be good for doing large splits (see north and south pole presumed reprojections, assuming that your original map was Equirectangular).
spole.jpgnpole.jpg

A generic split shows some promise, but the split lines would need a little refinement.
split.png