Following methods are unimplemented,

    @Override
    public String getName() {
       throw new UnsupportedOperationException("not implemented");
    }

    @Override
    public boolean isLoggable(System.Logger.Level level) {
        throw new UnsupportedOperationException("not implemented");
    }

    @Override
    public void log(System.Logger.Level level, ResourceBundle bundle, String format, Object... params) {
        throw new UnsupportedOperationException("not implemented");
    }

    @Override
    public void log(System.Logger.Level level, ResourceBundle bundle, String msg, Throwable thrown) {
        throw new UnsupportedOperationException("not implemented");
    }

Among those, getName() is used in JavaFX PerfLogger implementation. Implementing those would be trivial and straightforward.