I've had similar issues myself in the past.
What your HTML file is possibly doing is sending HTTP requests to Localhost in order to load resources (such as Pixi.js), not actually requesting files.
If not, Pixi.js may be doing that itself.
This is useful behavior on a web server, as some of the things it might be requesting could be generated dynamically, differ in response to cookies, or similar. XMLHttpRequests often go to this kind of dynamic content, and in this case the computer handling the request needs to know what to do with the file in order to generate the proper response.
(If they didn't, then server-side scripts would be unable to run, you'd just get a copy of the file.)
That is what the web server is there to handle.
The Flip Side
Similarly, would you want pages from the internet to be able to access all your local files? Run arbitrary scripts as they see fit? As other answers have implied, it is a huge security risk. That's why it's turned off by default. By setting up a web server you can allow access to specific files and not others, as well as specify how things are accessed or run.
What to do?
In your case, it's not so handy.
If there is a webserver recommended in the tutorial, I'd use that.
If not, I use Lighttpd.
There's also the python SimpleHTTPServer mentioned in another answer.
Hope this helps.