No it has more to do with internal fuel volume and aerodynamics ex: drag, lift, ect. One good reason the SU-35's range was increased was because of more room for internal fuel, more fuel equals more weight. And sorry but most of any aircraft is made of composites. Carbon/resin based composites aren't going to make a big difference in weight especially since the outer skin of flankers is made of thin lightweight alloys.
Newer avionics and engines can save a lot of weight when compared to older versions.
And by attack radius I assume that the article is talking about combat radius, in which case 1,000 km is not that great for a Flanker, albeit we are talking about heavier carrier based aircraft. This is not to down play the J-15 because 1000km is nothing to sneeze at even with conservative payload figures but we don't know the figures.
Weapons load and fuel figures are also not known, which effect range drastically. Are we talking a full combat load or half load with external fuel tanks? And this not only applies to Chinese aircraft but to every aircraft. I often find different performance date for the same aircraft depending on source, this is because the figures that were given were under different circumstances.