This may be an HTML issue. For a multiple select, the name of needs to end in “[]”, to signify an array. So try changing:
<select name="<?php echo $themename_option_name.'['.$valueid.']'; ?>" id="<?php echo $themename_option_name.'['.$valueid.']'; ?>" multiple="multiple" style="height:150px; min-width: 200px;">
to
<select name="<?php echo $themename_option_name.'['.$valueid.']'; ?>[]" id="<?php echo $themename_option_name.'['.$valueid.']'; ?>" multiple="multiple" style="height:150px; min-width: 200px;">
So you should end up with:
<select name="hurst_theme_options[hurst_content_bullet_cats][]" id="...