First thing's first:

##do not import an unofficial jQuery library forked by someone!

Now, when importing any script, you should always define the root of your site using `JUri::root()`. You should also use Joomla's `JHtml` method. So replace this:

    $document->addStyleSheet('modules/mod_marquee/css/style.css');
    $document->addScript('modules/mod_marquee/js/jquery-2.1.1.min.js');
    $document->addScript('modules/mod_marquee/js/jquery.marquee.min.js');
    $document->addScript('modules/mod_marquee/js/script.js');

with this:

    JHtml::_('stylesheet', JUri::root() . 'modules/mod_marquee/css/style.css');
    JHtml::_('script', 'http://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js');
    JHtml::_('script', JUri::root() . 'modules/mod_marquee/js/jquery.marquee.min.js');
    JHtml::_('script', JUri::root() . 'modules/mod_marquee/js/script.js');

I'm not sure which version of Joomla you're using by take a look at my [answer on another question to import jQuery properly][1]

As for you script, try using this at the beginning instead:

    jQuery(window).on('load', function($) {

else try using:

    jQuery(document).ready(function($) {


  [1]: http://stackoverflow.com/questions/12471067/importing-jquery-into-joomla/12473933#12473933