Idk if it's coloring or not, but yeah I think you can make the case that Kuma used haki here.
I wonder how tho, dude is basically a robot now moving on instincts.
I guess it's probably something like the machine shark, even though it's almost entirely a machine, controlled by the Satelites, it still has its shark instinct to eat its prey.
Kuma is much the same, but he has a father's desire to protect his daughter.
But how he realised she was in danger can't be explained logically.