The actual issue is not comparing modern, newly developed turbo diesel with ancient, 30 year old technology gas engines, is it? If diesels just coming out of research can rival today's gas engines in weight, it is probably time for the gas engine manufacturers to redesign their engines to get more weight out and beat the diesels. Inherently, gas engines will be lighter, since the stresses of 9:1 compression are much lower than 17:1 of diesels.
I would expect that the same tools that made diesels approach gas engines (CAD design, close attention to thermodynamic processes, water cooling, rotory technologies) should let gas engines reduce considerable weight and widen the gap.
Competition is good, let the games begin!