As I didn't get any reaction to my query, I looked at it further by myself.
For those who want to add the readmore button on the category blog listing (non k2 content), add the following code to /templates/gk_game/html/com_content/category/blog_item.php after line 53 -> <?php echo $this->item->introtext; ?>
Here is the code to add:
<?php if ($params->get('show_readmore') && $this->item->readmore) :
if ($params->get('access-view')) :
$link = JRoute::_(ContentHelperRoute::getArticleRoute($this->item->slug, $this->item->catid));
else :
$menu = JFactory::getApplication()->getMenu();
$active = $menu->getActive();
$itemId = $active->id;
$link1 = JRoute::_('index.php?option=com_users&view=login&Itemid=' . $itemId);
$returnURL = JRoute::_(ContentHelperRoute::getArticleRoute($this->item->slug, $this->item->catid));
$link = new JURI($link1);
$link->setVar('return', base64_encode($returnURL));
endif;
?>
<p class="readmore">
<a href="<?php echo $link; ?>">
<?php if (!$params->get('access-view')) :
echo JText::_('COM_CONTENT_REGISTER_TO_READ_MORE');
elseif ($readmore = $this->item->alternative_readmore) :
echo $readmore;
if ($params->get('show_readmore_title', 0) != 0) :
echo JHtml::_('string.truncate', ($this->item->title), $params->get('readmore_limit'));
endif;
elseif ($params->get('show_readmore_title', 0) == 0) :
echo str_replace('...', '', JText::sprintf('COM_CONTENT_READ_MORE_TITLE'));
else :
echo JText::_('COM_CONTENT_READ_MORE');
echo JHtml::_('string.truncate', ($this->item->title), $params->get('readmore_limit'));
endif; ?>
</a>
</p>
<?php endif; ?>