I have recently bought two 2.5 external cases, i see that they come with a different connection on the case to the lead. They look very similar to my Samsung phone so similat in fact i tried it using the normal micro usb lead and it worked.
On my my phone the small one is a video out via another lead but obviously that not the case on an empty case, unless there is software to make this so.
From what you’ve written regarding it fitting your Micro USB cable, I think you’re referring to a USB3.0 Micro-B port - a very strange looking connector designed so that an older cable could still be used if required.
No worries - for viewing the movies easily and cheaply from the drive, I would suggest one of the surprisingly good Sumvision range of Media Players, I use the Micro 4 at home but they start at a really low price if you don’t need wireless/network streaming built in. This one’s £20