On IRC LSorensen suggested I add my username to the audio group. He also informed me that the alsaplayer-alsa package exists. I installed the other package and added the audio group and now both programs produce sound. I cannot get sound out of XMMS yet but I will play with it when I get more time.
Note that the "output plugin" setting in the XMMS preferences controls which driver is used to play sound.
This was my missing ingredient. Choosing the ALSA output plugin option has enabled me to hear the wav file I was using for a test. Now I need to spend some time with actual music files ;-) Richard