The difference you're seeing is related to the version installed. I checked your version page and installed matching versions and got similar output to what you have -- and it played.
A direct download of your ogg file shows that it is, indeed, silent.
That leads me to think that the problem is somewhere outside of MediaWiki.
At this point, I'm not sure what to look at. Since I am testing this on a virtual CentOS box on my laptop, I went ahead and uploaded a list of all the packages I have installed. Maybe you'll be able to spot something in there.
The other thing to do is to try running the command to convert the midi file to an ogg file yourself. You can find the commands by looking at your debug log and duplicate them.
For example here's what I see if I look for wfShellExec in my debug log:
$ grep wfShellExec images/debug.log | tail -5
wfShellExec: /bin/bash '/var/www/html/w/includes/limit.sh' 'LILYPOND_GC_YIELD='\''25'\'' '\''/usr/local/bin/lilypond'\'' '\''-dsafe=#t'\'' -dbackend=ps --png --header=texidoc '\''/tmp/MWLP.e8f63cbbbf327ecd7fe9f86157c73e0a/file.ly'\'' 2>&1' 'MW_INCLUDE_STDERR=;MW_CPU_LIMIT=180; MW_CGROUP='\'''\''; MW_MEM_LIMIT=307200; MW_FILE_SIZE_LIMIT=102400; MW_WALL_CLOCK_LIMIT=180; MW_USE_LOG_PIPE=yes'
wfShellExec: /bin/bash '/var/www/html/w/includes/limit.sh' ''\''/usr/bin/convert'\'' -trim '\''/tmp/MWLP.e8f63cbbbf327ecd7fe9f86157c73e0a/file.png'\'' '\''/tmp/MWLP.e8f63cbbbf327ecd7fe9f86157c73e0a/file-trimmed.png'\'' 2>&1' 'MW_INCLUDE_STDERR=;MW_CPU_LIMIT=180; MW_CGROUP='\'''\''; MW_MEM_LIMIT=307200; MW_FILE_SIZE_LIMIT=102400; MW_WALL_CLOCK_LIMIT=180; MW_USE_LOG_PIPE=yes'
wfShellExec: /bin/bash '/var/www/html/w/includes/limit.sh' ''\''/usr/bin/timidity'\'' -Ov '\''--output-file=/tmp/MWLP.e8f63cbbbf327ecd7fe9f86157c73e0a/file.ogg'\'' '\''/tmp/MWLP.e8f63cbbbf327ecd7fe9f86157c73e0a/file.midi'\'' 2>&1' 'MW_INCLUDE_STDERR=;MW_CPU_LIMIT=180; MW_CGROUP='\'''\''; MW_MEM_LIMIT=307200; MW_FILE_SIZE_LIMIT=102400; MW_WALL_CLOCK_LIMIT=180; MW_USE_LOG_PIPE=yes'
wfShellExec: /bin/bash '/var/www/html/w/includes/limit.sh' 'GIT_DIR='\''/var/www/html/w/.git'\'' '\''/usr/bin/git'\'' show -s --format=format:%ct HEAD' 'MW_INCLUDE_STDERR=;MW_CPU_LIMIT=180; MW_CGROUP='\'''\''; MW_MEM_LIMIT=307200; MW_FILE_SIZE_LIMIT=102400; MW_WALL_CLOCK_LIMIT=180; MW_USE_LOG_PIPE=yes'
wfShellExec: /bin/bash '/var/www/html/w/includes/limit.sh' 'GIT_DIR='\''/var/www/html/w/extensions/MwEmbedSupport/../../.git/modules/extensions/MwEmbedSupport'\'' '\''/usr/bin/git'\'' show -s --format=format:%ct HEAD' 'MW_INCLUDE_STDERR=;MW_CPU_LIMIT=180; MW_CGROUP='\'''\''; MW_MEM_LIMIT=307200; MW_FILE_SIZE_LIMIT=102400; MW_WALL_CLOCK_LIMIT=180; MW_USE_LOG_PIPE=yes'
$
Copying everything after "wfShellExec:" gives me something I can put in a shell file and duplicate and actions.
There may be some interesting output there.