You're right, it doesn't work the arms much. A lot of posture problems are caused by imbalances between the back and chest. When people work their chest out frequently but neglect their back, it causes the chest to tighten and pulls the shoulders forward. This workout tries to balance out this problem by working the back more.
I wouldn't add any bench press to the program. I think on either the 3rd or 4th day they have a close-grip bench press in there. Also, this is one of the imbalances the program is trying to fix. I don't think there is anything directly targeting the arms in this, it just uses them to support the target (synergist muscles). I have a tendency to stick with the program as designed, but I suppose it wouldn't hurt to add a round of curls or chin ups.
I hope it works out for you. Let me know how it's going in a month or two.