From help I got from the oXygen forum, I've determined that the problem is that the JRE in the oXygen installation is 32-bit.

It was the teideb package repo that presumably gave me my oxygen install (I didn't do anything else to get oXygen installed). The package would seem to be: tei-oxygen_12.1-tei1_all.deb from here: http://tei.oucs.ox.ac.uk/teideb/binary/ which contains a complete oXygen package (in data.tar.gz) which does indeed include a JRE.

I just moved the JRE elsewhere, so now it's presumably using the installed Sun Java. But I'm getting another error now:

    using oXygen XML Editor stylesheet documentation generator.
    Exception in thread "main" java.lang.ExceptionInInitializerError
    at ro.sync.xsl.documentation.XSLStylesheetDocumentationGenerator.main(Unknown Source)
    Caused by: java.lang.RuntimeException: The preferences directory: /root/.com.oxygenxml
    cannot be accessed !/n Please check the read/write access on that folder and its ancestors !

There is no such directory, of course. The Jenkins process that's initiating the stylesheet script file is apparently running as root, so perhaps that's why it's looking there for preferences, but this is a headless server that doesn't need any GUI layout information. What would it be looking for in the preferences directory? I've posted for help on the oXygen forum.