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    your welcome.
I think you should do some customization by your own because this kinds of permissions would be very detail.
in general if a user is a module admin he/she can access to all details of that module (here: news)
I test some modification in my local site and i think you can do this by your own.
firstly i assume You want to allow all users have access to system module (like webmaster group) to see counters. 
because if a user have access to system module he/she can do anything and see everything.
So you can add the below code wherever in news/admin/index.php to find if the current user is webmaster or not.
 global $xoopsUser; 
$groups = is_object($xoopsUser) ? $xoopsUser->getGroups() : XOOPS_GROUP_ANONYMOUS; 
$gperm_handler =& xoops_gethandler('groupperm'); 
 
$isWebmaster = $gperm_handler->checkRight('system_admin', XOOPS_SYSTEM_USER, $groups);  
Then you can use above variable for each counter like this:
for line 166:
$counters= $isWebmaster ? $eachstory -> counter() : 'No perm';
then use this: 
" . $counters . " | im not a coder so maybe one developer can edit my codes or show you easier way but im sure the principles are correct.