From the FAQ section at Dire Studio's page for their Shutter Count application as of August 2015:
The EOS-1D X Mark II, EOS 5DS, 5DS R, 80D, 750D / Rebel T6i / Kiss X8i and 760D / Rebel T6s / 8000D cameras do not provide shutter count information. It seems that Canon has removed the shutter count functionality from the remote control interface.
If that is in fact the case then the only way to get a shutter count from the camera would be to send it to a Canon Authorized Service Center.
Dire Studio has released ShutterCount version 3 (currently for Mac or iOS only) that can now read the shutter counts for the cameras excluded above, as well as some other more recent models. From the updated FAQ page as of July 2, 2017:
Q13 - The shutter count is not displayed for new cameras (5D IV, 5DS/R, 1D X II, etc.)
Update to ShutterCount 3.0 or later on your Mac or iOS device. The Windows version will support these cameras later on.
For a list of all supported cameras, please see the Compatibility List at the ShutterCount Tech Specs page.
Dire Studio also now offers an add-on Live View Pack to their Shutter Count app that allows one to see Live View stills and Live View movie actuations of the shutters in selected cameras.
From a comment below:
Do you know how they get that information? If what they say in the initial quote is true (that the camera does not provide shutter actuation count information), how can they work around that? Or did they simply not know how to read out that information? I do not have an Apple device, I guess I'll have to wait for the updated Windows version
My understanding is that the newer models covered in version 3.0 still do not include shutter count functionality from the remote control interface. (The interface provided by the Canon Software Developers kit or SDK). Someone was either able to get code beyond the SDK from Canon or they managed to hack/reverse engineer it. Unfortunately, it doesn't look like Dire Studio is interested in ever updating the Windows version again, due to the high cost of Microsoft licensing. They once had a statement to this effect included in one of the FAQs, but it seems to no longer be there at their site.
As of 22 February, 2018 there has still been no update to the Windows version of Shutter Count. In fact, the older version compatible with Windows is no longer offered for sale by Dire Studio.