He should definitely have it now after the Lich battle. I think several others should gain some war skills as well. I am very interested to see how Yoshi leveled up.
Hopefully he goes to the barracks and gets it right away. If he doesn’t have it after the battle. Did he lead many in the battle so he could earn it? I assume that’s how you earn it. I’d like to see he rewards the different folks in town got. Especially the leader of the guards.