I was playing a game the other night and came across this situation. My opponent declares a military challenge I defend and lose do I kill the defending character for the old way and then kill one for the military claim. Or can I kill the defending character for the military claim so that I don't have to kill anyone for the old way?

P.s. I kind of think it plays out like deadly where I can kill the character for a military claim and not worry about deadly?

It plays out very much like deadly - it's a passive as well. Claim happens first, and, once claim is satisfied, deadly/the old way can only affect any remaining (non moribund) characters. If you defended with only characters you've killed for claim, deadly/the old way won't do much.