Ubuntu 18.04: AppImage can't open any files

Ubuntu 18.04 ships an ancient version of MKVToolNix (19.0.0), which doesn't provide all the features I needed, so I tried to use the AppImage.

$ ls MKVToolNix_GUI-38.0.0-x86_64.AppImage 
MKVToolNix_GUI-38.0.0-x86_64.AppImage
$ chmod +x MKVToolNix_GUI-38.0.0-x86_64.AppImage
$ ln -s MKVToolNix_GUI-38.0.0-x86_64.AppImage mkvmerge
$ ./mkvmerge --version
mkvmerge v38.0.0 ('The Silent Type') 64-bit
$ ./mkvmerge -i sample-file.mkv
Error: The file 'sample-file.mkv' could not be opened for reading: open file error.

I tried adding the APT source for 18.04 instead, and the official 38.0 package works just fine, so this is definitely an issue with the AppImage.

It's kind of ironic: I still run static binaries compiled over a decade ago with no issues, but I've had nothing but trouble with AppImage which was supposedly going to "solve" the distribution problem.