HI Wolfgang!

Does "/usr/bin/notify-send ..." work when you start it from command console ?
If that is ok make a simple alert to specific callsign (not partial call) and start cqrlog with cqrlog  --debug=1 > /tmp/debug.txt
You should be able to dig words "Spot is" and "Call alerting is" from debug.txt after alert should have been done.

The text is produced by:
if dmData.DebugLevel >=1 then Writeln('Spot is:',spot,#$0A,'----Call alerting is: ',call,',',band,',',mode,',',freq,',',freeText,'-----------');
dmDXCluster.RunCallAlertCmd(call,band,mode,freq,freeText);

And after that RunCallAlertCmd is executed.
The RunCallAlertCmd has also debug texts that should follow those texts above:

Either this if executable is not found:
if dmData.DebugLevel>=1 then Writeln('AProcess.Executable: ', paramList[0],' Not found!');

or this if it is found:
if dmData.DebugLevel>=1 then Writeln('AProcess.Executable: ',AProcess.Executable,' Parameters: ',AProcess.Parameters.Text);

Wit his information you should catch the point where alert fails.