Obito had to have used kamui because I'm pretty sure Kakashi is unable to take himself into the dimension as he's never done it in the past and has only used it as a ranged attack. Obito can warp himself and others that he is touching. It's possible Kakashi used it on Obito and Obito used it on him at the same time, though I'd say it's more likely Obito grabbed Kakashi and used it on both of them.