If you're using the app directory, page.js is just the file name to identify a page. The folder names are what allow you to define dynamic routes, catch-all routes, layout groups, parallelized routing and so forth. If a folder doesn't have a page.js file as a direct child of that folder then it won't be considered a route. Furthermore, with the new app router you can include components and folders within the app directory as long as their namespace isn't taken. I hope that addresses your question here.

As far as the old approach is concerned, I'm not too sure. I'm unfamiliar with the code you've pasted in your example, which leads me to believe it's older than me or that perhaps the code (if generated) was coming from the React-Router package which handles client side routing.

If it's not mentioned in the docs, then It's my understanding, unless you download older versions of nextjs, then you cannot do what you're trying to do exactly as you've provided in your original example.