OK. I loaded up the same MKV and took note of what was different on my HB screen vs. yours. Everything is the same when I click the Apple TV 3 preset. Then, I rendered one chapter with those settings and opened it in Quicktime, "Windows" (menu), "Show Movie Inspector". "Current Size" shows as 1914x800 (which is definitely not 720p).
If you open it in Quicktime and it shows a 720p number (something at or less than 1280x720), it continues to imply there's something wrong with the MKV file. I'd locate the disc and use MakeMKV anew on it. Don't do any other processing after that with any other software. Then, run that through HB as usual but maybe cut it to just one chapter or one minute to see what resolution will come out (before rendering the whole movie).
Also try clicking the generic Apple TV 3 preset too (for 1 chapter) so that we can rule out anything that might be wrong in your custom preset settings.
Then, open both in Quicktime, "Windows" (menu), "Show Movie Inspector", "Current Size" and see if either gives you 1914x800.