Hi Aleksandar,
Thanks for posting a clear explanation of your problem, and especially for posting the solution once you found it. Those HTTP headers should indeed be set when making all JSON requests to the API. Some tools do this automatically for you; I see you're using Postman, which I guess doesn't.
Because Shopify doesn't know how to correctly parse your payload, the errors it will return are somewhat unpredictable. It might help others who run into this issue if we added that information to our own API documentation, so I'll look into getting that done.
Thanks again!