Good news, everyone! I fixed it by changing output: 'app.cjs.js' to output: 'cjs'. It looks like the plugin just doesn't like .js in the output name.
To demonstrate bug:
> npm install
> broccoli build dist
Error: ENOENT, no such file or directory '~/broccoli-es6-module-transpiler-bug/tmp/compile_modules-tmp_cache_dir-jbRvJdUD.tmp/0/app.cjs.js.map'
at Error (native)
at Object.fs.lstatSync (fs.js:716:18)
at Function.symlinkOrCopySync (~/broccoli-es6-module-transpiler-bug/node_modules/broccoli-es6-module-transpiler/node_modules/symlink-or-copy/index.js:19:12)
at ~/broccoli-es6-module-transpiler-bug/node_modules/broccoli-es6-module-transpiler/index.js:252:23
at Array.forEach (native)
at CompileModules.copyFromCache (~/broccoli-es6-module-transpiler-bug/node_modules/broccoli-es6-module-transpiler/index.js:247:28)
at CompileModules.compileAndCacheModules (~/broccoli-es6-module-transpiler-bug/node_modules/broccoli-es6-module-transpiler/index.js:240:14)
at CompileModules.<anonymous> (~/broccoli-es6-module-transpiler-bug/node_modules/broccoli-es6-module-transpiler/index.js:150:14)
at $$$internal$$tryCatch (~/broccoli-es6-module-transpiler-bug/node_modules/broccoli/node_modules/rsvp/dist/rsvp.js:470:16)
at $$$internal$$invokeCallback (~/broccoli-es6-module-transpiler-bug/node_modules/broccoli/node_modules/rsvp/dist/rsvp.js:482:17)
Build failed