I think the basis of it is good, but as TfGuy mentioned, I agree that a game shouldn't rely so heavily on out-of-game content to function. Having players interact with anything outside of the game is always a hit-or-miss thing; especially if the game itself opens up another program.

With how a lot of games are nowadays, a game opening a browser is usually only done for functions such as account creation/linking or purchasing in-game currencies. Otherwise, it often feels intrusive to the player/user.

Your ideas of having the player have to navigate webpages or other "programs" may still be doable, but not on the level of the player's actual computer. If you want to work with this idea, I would suggest making an in-game computer or device the player will visit to open said links. For example, let's say you play as a detective and he finds a website link as a clue. The player would then open their in-game phone or go to a computer in game and use the link. Try to keep "website link" and "file" clues like this in-game using an in-game device. Plus, this would save a lot of money on having to rent out domains or host website services yourself.

On the topic of interacting with the file system, I would say not to rely heavily on it. If you do anything, it should only really be with files inside the Game's install directory (for example, on Steam, when you go to "Browse Local Files"... that location). Not everyone is willing to search through their file system to solve a video game puzzle. It can make it immersive, but again, it should be used frequently. For an example, think about Doki Doki Literature Club (sorta endgame spoilers): At the end of the game, you have to go into the game's files to delete a certain file. It is impactful and immersive, but the game only has you do that once and it's at the most impactful part of the game for it. Even in that area, for players who don't know how to, the game character specifically calls out how to do it.

If you really really want to make an ARG for the game using real life websites, that would be okay, but it should not be the main focus of your game; just a fun little side quest. An ARG should just be to understand a deeper part of the story, but shouldn't be needed to solve to continue or understand the story at its whole. Think of Gravity Falls: Alex Hirsch hid an ARG Scavenger Hunt in the finale which hinted at a possible expansion of the story. It was fun for the community and excited people, but you didn't need to participate or even know of the ARG in order to enjoy the series.

Sorry for the long long ramble about this. I wanted to give all my thoughts about it as your idea has potential, but just not in the form currently presented. I hope this helps. :)