Maybe he still cares, and a lot too. But he's clearly not at the point of trying to get that ring at any cost. He's not ready to sacrifice his roll, his touches, and his points.
He doesn't have that explosiveness any more. He's making more and more difficult shots, because he works hard on his shooting to compensate for his digressing athleticism. Those tough shots were easy for him, years back, because he would simply blow by defender or rise a lot faster than defender.
Under such circumstances, I would have hoped and kind of expected, that he would try to involve the big a lot more from the beginning. Let them be the main charactors in the first 3 quarters, and he takes over in the 4th. He still can be the hero, and those bigs would be a lot more interested in playing defense in the 4th.
You got to reward your big men, in order to raise their energy level at the defensive end. Kobe is not doing that. That's why I am no longer convinced that he REALLY want that 6th ring above everything else.