In Windows, default applications are registered either by URL scheme (so ftp, http, https, gopher...) or file extension (.txt, .html, .pdf, .mp4...). As far as I know there is no special registration for "browsers" specifically, you just register your application as a handler for whatever protocols and file formats you want.

So if you want to make your random executable be "a browser", my guess is you should register it as a handler for http, https, and .html, at least.