Is a storm collar required on the metal flue and laundry pipes in the photo?
I would say yes.
Based on…?
Based on the storm collar will most likely leak otherwise. The storm collar is bent downward, like an umbrella, over the junction.
No.
You need a storm collar with a rigid roof jack because the vent and the jack move independently (i.e., the jack is connected to the roof structure and the vent to the appliance). The TPO jack is flexible and does not have the same issue.