Yeah, but in the manga, it wasn't just a bear killing thing.
Kite hung out with Gon for, like, months back then basically teaching him to be a Hunter. He's the one who ACTUALLY inspired Gon to become a Hunter and was really more of a father to him than his actual father was.
All of that was in the original anime series, but not in this one. So his insane reaction doesn't make sense here. Kite is a guy he met once as a kid, and then recently went on one mission with. He's had a grand total of a few days worth of interaction with the person. This whole thousand yard stare thing he's doing just doesn't feel warranted in this situation because of it.