I think better to make it visible in the main homepage on both situations so new players/new comers who visit the site for the first time will be easier to explore the site without an account.
I second this. What's the reason why it's hidden for a guest anyway? Is it simply because those menus need you to log in to access them? I still think having a navigation bar for guest accounts would be more helpful. Scrolling down to see the content of the website is not a nice experience. Maybe Chips can modify or show a notice if some pages are not available for guests. I don't think having a home button or something similar is too much to ask for.