Give permission to non-admin user to view and edit list of orders
After comparing the query being executed for the admin user and the non-admin user I found that 1=0 is being added to the commerce_orders view's query. 

Further checking out the code, it seems that in the commerce.module file, the code expects either shipping or billing permission being granted to the user.

After adding one of them, the list was visible. I don't know why it's like this, List of orders must not expect that permission right?

TLDR; Adding the billing/shipping permission fixed the issue.