Thanks for the feedback. Rank is your global rank in popularity score*. It only appears if your rank is less than 10k. The rank determines the order in which you appear in the browse pages on itch.io. It was not added to give you a way to compare yourselves with other games, it was added to give you some more insight in how games appear on the global listing page, and give you a way to measure progress against yourself as you might experiment with promotion. (For example, what happens if you tweet about your game, or release a new update, or write a blog post, what will happen to your rank?)
We have not announced this feature yet, we've pushed it out with some slight redesign to the project edit pages. We tend to make incremental changes to pages until we're happy enough to announce them on our blog. A new goal of ours going forward is to give developers more insight on how their projects are performing, since we want to encourage people to build the best possible pages.
A lot of developers are using itch.io as the place to launch their games to the world, and we want to make sure they have the knowledge to get their game in front of the most people. A lot of components on itch.io are optional: designing your page, adding tags, classifications, building a community, etc. We've seen many developers do the bare minimum in putting together their page, then being disappointed because they didn't get enough views to match their expectations. This really puts them off to the platform.
We see this as our fault a lot of the time because we don't give developers an opportunity to understand how the system works. When I first launched itch.io I was "anti-discovery", there was no way to browse games since I thought developers could bring their own audience. I see now that this is silly, we should be helping. Our game listings are very important for smaller creators to build their audience. It's a really powerful thing given that it's already super hard to get attention on other platforms.
We want to make it very clear how you boost your game's discoverability on the listings, so we want to make this rank number available for those that will find it useful. If that's not a priority for you then that's perfectly okay. We can see many benefits for a lot of developers though. It gives them a path to presenting their page in the best way possible. Additionally, those who come to itch.io and see higher quality works are more likely to revisit additional pages, follow you, add to collection etc.
I definitely understand why you're put off by it though, and I do appreciate your feedback. If we do end up keeping it there then it's unlikely we'll have a option to turn it off, since we want to avoid more UI options than necessary.
*Popularity score is a ever changing value that represents how popular your game currently is, it tends to fluctuate a lot since it's sensitive to things that have happened to your game in approximately the past two weeks.
Sorry for the essay, I hope this clears things up though!