Yes, the browser version is completely free to play online. Third-party APK versions are also typically free, though they may include ads.
If you want the official Zombotron experience on your Android phone, is the best and only official option. It is available for download on the Google Play Store. zombotron 2 time machine download for android
While not a "download," some sites host the game in a way that mobile browsers can technically load it, though they often lack touch controls: Yes, the browser version is completely free to play online