OK, time for an update. This is a really strange bug.
First I have to admit that it was dumb that I didn’t immediately try other HEVC videos. But hey, it was late yesterday and I was pretty wasted 
Anyway, when I got home from work today, I tried to play other HEVC videos. And they all played fine!
So I encoded some other video with the same settings I used yesterday…and again it didn’t work correctly in both players.
My next guess was that maybe Opus-audio in the MP4 container is the problem. So I did an encode with a matroska container instead, but still the same.
So I thought maybe it’s the combo of HEVC/Opus. I did AAC instead of Opus in a matroska container and suddenly it worked! BUT: AAC in a MP4 container again gave me the faulty playback 
I’m completely out of ideas now.
Here’s how it looks (and sounds 
) like when I try to play the video on VLC and Dragon Player:
Here’s how it should look and sound:
And here’s the file if anybody wants to check:
BTW: It plays absolutely fine on my phone 