Why is there a version # below the download links on my page but I don't see it on others? Is that only visible by me?
The version number is included when you use butler to upload your game. It's public information. You can set your own version with the user version flag: https://itch.io/docs/butler/pushing.html#specifying-your-own-version-number
Why don't I see it on other games?
Probably because a lot of games (and build updates) get uploaded without using the Butler tool. I know I'm guilty. I've been meaning to set butler up for ages now.