On your server is easiest, especially if your host provides cPanel access.
Log in to your accounts cpanel, start up phpmyadmin, select your database, select the table, mybb_forums.
Browse first, look at the values for usepostcounts. If it's already set to 1, there's nothing to change.
Otherwise, click the SQL tab and enter your update query.
UPDATE mybb_forums SET usepostcounts = 1;
There will be an button to SIMULATE QUERY so you can see how many records will be changed. If all is as you expect, click the Go button to make it happen.
All that said, I don't believe you will fix your problem that way. Your problem is views, not post count.
The new 1.8.27 added some conditionals that influence the forum view count.
I'm still on 1.8.26 and do not have experience with the new settings yet.
I observe that, with 2 exceptions, all threads in NEWS DEPARTMENTS forums created or posted to before 9/16 approximately 12:54pm have view counts. Threads and posts after that date have zero views. Something changed on that date. Whether it was a plugin or something else, I can't see. But there's your first clue. I did not continue to look in the other forum groups.
Your next clue might be in seeing what core files have been changed. (whether a manual edit or changed by a plugin). AdminCP / Tools and Maintenance / File Verification.
Your next answer might be from asking of the community in general "Has anyone seen the view count not change in forumdisplay with a new installation of 1.8.27?"
I can't answer that, I have not yet updated.
Finally, I also observe that guest views don't count, but neither do member views. I signed up, viewed the truck overturn news item, replied to the thread, and the view count did not change.
So, if file verification shows no changes to forumdisplay.php or showthread.php, then the only other place I could think is in the templates.
AdminCP / Templates and Style, click Templates, then tab Find Updated Templates. Look for forumdisplay_thread in your current theme. If it is not listed there, then it is most likely unchanged. But you could go and look at its coding. You're looking for 2 lines similar to
<td align="center" class="{$bgcolor}{$thread_type_class}"><a href="{$mybb->settings['bburl']}/misc.php?action=whoposted&tid={$thread['tid']}" onclick="MyBB.whoPosted({$thread['tid']}); return false;">{$thread['replies']}</a>{$unapproved_posts}</td>
<td align="center" class="{$bgcolor}{$thread_type_class}">{$thread['views']}</td>
{$thread['views']} is the variable that shows the thread views currently being counted.
Since some older thread views are not zero, then the template is most likely ok.
Showthread.php is where the views count gets updated.
In AdminCP / Configuration / Show Thread Options, what is your setting for Delayed Thread View Updates? Is it On or Off? Set it to Off. If it is On, thread view update occurs every 15 minutes with the Task Manager / Thread Views.
If it is supposed to update as a task, and your theme has been edited to delete the required code at the bottom, then the task is not running, hence no update.
Try this as a double check. AdminCP / Tools and Maintenance / Task Manager / Scheduled Tasks, locate Thread Views task and click the associated Run Task link. View the forum to see if it updated.
If that's the case, you need to fix the theme or change the Showthread option I mentioned earlier.