@Lynne and I commented on this just the other day in another thread. This would require something like the "showpost.php" module to be resurrected or an event (such as a click) on the "showthread" module when the user decides to view a post, otherwise how would you differentiate that the user was reading a particular post. Yes, it could be done, but only with a functional change on how you view posts/threads.
When a thread/post is viewed, the current "read-time" is stored and the assumption is made that all prior posts within the thread have been viewed.
--------------- Added 19 Sep 2014 at 14:46 ---------------
If this is a vBulletin board they are most likely fudging the numbers. They can count the number of posts the poster has posted, and they can multiply it by the number of thread views of the threads which contains the posts. That would create a very large number very quickly. I don't believe they are actually tracking who has read a post, but of course I could be wrong -- it is possible.
On one of the boards I run, I somewhat accurately track posts: when the post was read, how long they were sitting on the post (post_read_time), consecutive posts read in the thread, order of the posts read in a thread, and other statistics. This required a complete rewrite on how threads and posts are displayed and cached. All this overhead would probably kill the average hosted board. The method that vBulletin uses is efficient, and you would require a real need in order to justify the additional overhead.
Thanks for the reply. It's a vBulletin board and I' am with you, I think they are fudging the numbers. The pay-off is some people would like to believe their posts are being read thousands and millions of times.