To properly answer your question, it'd be helpful if you posted a link to the full WP config file and an example of the file that's being processed.

Also, you mentioned you're only using WP to create a CSS file, does that mean you're just trying to use something like SASS, Stylus, Less, etc? If so, you could probably just set up a package.json script to compile your CSS without WP.
For example, if you have a .scss file, you could install node-sass, and create a simple Node script to compile what file you pass in as an arg.

bin/
  - build-css.js
src/
  - styles.sass

Within build-css.js

#!/usr/bin/env node

const { basename, resolve } = require('path');
const sass = require('node-sass');

const [...files] = process.argv.slice(2);

if (files.length) {
  files.forEach((relativeFilePath) => {
    const fileName = basename(relativeFilePath, '.scss');
    
    sass.render(
      {
        file: resolve(__dirname, relativeFilePath),
        outFile: resolve(__dirname, `./public/css/${fileName}.css`),
      },
      (err, result) => { console.log(err); }
    );
  });
}
else {
  console.log('No files were provided to process');
}

Within package.json

"scripts": {
  "build:css": "node ./bin/build-css.js"
}

The above has the benefit of giving you the control of how your files are processed at a more granular level, and you're only locked in to any SCSS changes, instead of Webpack and SCSS.

If you're using WP for it's file watching capabilities, you could instead wire up chokidar to run the new script when you change files.