I think that the issue you're describing already exists regardless of whether or not we show the number on the analytics page. This number has existed in our backend for a long time since it's how we sort things on any browse page by default. We want to make it more transparent because we think that the average developer is going to see it an an opportunity to have an impact on how more exposure we are giving them.
We have a policy cheating your ranking on the listings, your game gets de-ranked. We will continue to identify any suspicious pages and take appropriate moderation action if necessary.
Regarding the destruction of the culture because of people trying to optimize their rank. It's interesting idea but probably too speculative at this point. We still do a lot of curation on many parts of the site and we try to keep things fresh there. Popularity is already a loaded metric since something doesn't have to be good to be popular. Maybe in the future we'll change our algorithm for ranking games in order to combat this.
I'm interested in the idea of having another metric as a replacement. Some more stats that we plan on introducing in the future are impressions and clicks. Impressions being the number of times your game's thumbnail has appeared on our browse pages, and clicks being the number of time someone clicked on it. With that you can get an idea of how much exposure you're getting from us, and what your click through rate is. I'm not sure if it fulfills the same information as a rank number, but it's useful information to have