Apparently, one has to use the somewhat crude "ADT" command-line tool to build an app that uses Native Extensions.
Unfortunately, I cannot get past the numerous errors ADT is throwing at me. The latest is:
unexpected failure: inputs not set
java.lang.IllegalStateException: inputs not set
Unfortunately, I'm not an advanced developer, so I really don't know what any of that means. (But I'm sure if I can just get this one example to compile and run, I'll be better able to perform the necessary tasks in the future.)