Apple did away with streaming iTunes content (paid content) from portable external storage devices when later versions of iOS 8 were introduced and this hasn't changed since.
I have a decent collection of iTunes purchased movies I purchased that I used to be able to stream from my portable Seagate Wifi drive that I can no longer stream my purchased content from, any longer.
Very, VERY upset about this!
Apple only allows Home Sharing streaming from iTunes ( which IS NOT a hidden feature, btw) from any of their computers (which is kinda of moot point, somewhat, when your Mac is a MacBook as you CAN play all of your iTunes movie content on the go from those computers fine and can even home share the movie content, on the go, to an iDevice connected up to a TV with proper adapters and cables.
If you own a desktop computer, home sharing streaming IS limited to your home and home Wifi network. Kinda unfair to Apple desktop computer users.
So, I decided until Apple changes this policy, I've gone back to purchasing actual DVD/BluRay combo discs packages where I can do as I wish with the movie/tv content that I purchase on physical discs.