Why do you think it's clear that Kane's role is different from eriksen, lamela and Chadli based on those maps? Kane, Chadli and eriksen all play most of the game from midway between the edge of the centre circle and the opposing D, just on different sides. With lamela slightly deeper. Are you seeing something different to how I've explained?
For me, based on watching games (and I don't think this is a surprise to anyone, or some sort of amazing insight!!), Kane's starting position is higher up the pitch on the last defender, but he drops deep from there, the three behind start deeper but make breaks / runs to join and go beyond Kane. The net "heat map" effect is pretty similar for all 4 players based on those pics.