Now we’re talking. Doom was a massive deal because of the violence (as you mentioned), but also because it moved entertainment revenue away from MSM and onto PC’s and the internet.
Doom was not some watershed moment in entertainment. It was a trend setter, or at least a meme, in the industry but it didn't somehow change the trajectory of the game industry.
The PlayStation was vastly more influential on the industry on the whole than Doom. It was less expensive than PCs yet had a good selection of the sort of "mature" titles (or even ports) typically found on the PC. The PlayStation was not a platform that moved money from the "MSM" since it Sony which was the very definition of mainstream.
Doom was cool but it didn't even come close to doing what you suggest. It didn't even have Internet multiplayer until Kali (originally iDOOM) came up with their IPX/SPX bridging years after its release.
While id was certainly an Internet aware company in 1993 most consumers were not.
Keep in mind in 1993 a minority of households even had computers. A minority of those users even had modems. Even when they did have computers with modems connecting to a "local" BBS could still be a local toll call.
A copy of that month's PC Gamer was much cheaper than a modem and got you not just Doom but hundreds of megabytes of other crap. Cover discs were still a big deal even towards the end of the decade where home Internet access was more common.
As for the PlayStation, it was released in the Japan in 1994 and the US in 1995. Doom was released at the end of 1993 so it's contemporaneous with the PlayStation. The PSX had Doom-quality 3D games (including Doom itself) for a fraction of what a good Doom running PC cost.
