Look on exrx.net for the Arnold Press. That's more like the RKC military press.
Someone correct me if I'm wrong, please, but I believe part/all of the reason for the way the RKC military press works is due to the shape of the kettlebell itself - the weight is not centered, it tends to pull your arm back, so rotating and pushing out seems to help counter that tendency.
I think it's harder to do it your way so if your kettlebell is light for you that may be a reason to press straight up. I have to press outwards on a heavy kb military press - that can make the difference between the weight going up or not for me. I can't say whether it works that way for everyone but you might try a heavier bell and see if it makes a difference to you.
-S-
http://www.kbnj.com