Their recommended process is :
1. Install fasttext (it's an official Debian package, but you have to compile it on Windows).
2. Download and uncompress the LanguageTool release.
3. Create a config file.
4. Launch the server with the java command (of course, a JRE must be installed).
5. Connect to the API, e.g. with the browser extension.
Running a ready-made docker image replaces steps 1-4 and removes the need to install Java globally. Some will prefer it this way.