I might not be a gamer today if Playstation hadn't happened. Let's go down the proverbial alternate timeline of what-if's.
Xbox wouldn't exist either:Without Playstation, I don't think Xbox would have happened. At least not as soon as it did. That would leave Atari, Sega, and Nintendo. Why Atari? Why Sega? This goes back to my theory/belief that the industry can only sustain the top three gaming competitors. In our timeline, Sony knocked out Atari as the weakest link and Microsoft knocked out Sega as the weakest link. Without Playstation and Xbox, both Atari and Sega would have made it into the 2000's with their hardware.
Dreamcast\Consoles:Dreamcast may have looked different internally. I think that Sega would have had a bit more time to develop it, and thus, the Dreamcast would have been closer to PS2 power if it had waited an extra year to launch. Continuing with this, we would have had Shenmue complete on the Dreamcast as it would have had a full lifespan of 5-6 years, instead of 2 years. Certainly there would also be at least one successor to the Dreamcast.
I believe we would have seen Sega VR release either on Dreamcast or its successor. Sega was always pushing the tech envelope and had a VR headset developed for the Genesis. The... GENESIS!!!. It was cancelled due to motion sickness being an issue for obvious reasons. That said, I think we would have had VR before we did in this timeline.
Game Gear Successor:Sega would have probably created a successor to the Game Gear. I think it essentially would have been a direct competitor with the GBA and (jumping down this rabbit hole), had original Game Gear backwards compatibility similar to what GBA did with the GB and GBC.
I think Atari would still be hurting regardless of Playstation released, but I think we would have seen one successor to the Jaguar before the company went under as a console creator.
Personal Affect:Now, why would I possibly not be a gamer today without Playstation? Gaming changed on Playstation. The first Playstation changed the industry not just from a technical perspective, but also from the perspective of how gaming stories were told. Games like Resident Evil and Tomb Raider were on the Saturn as well, sure, but it's other games like Metal Gear Solid, Parasite Eve, FF7, Oddworld, Heart of Darkness, Dino Crisis, etc. etc. etc. This is the generation that started the narrative driven single player games and that is what my favorite genre is.
You could see some story telling on N64 and some on Saturn as mentioned above, but both Nintendo and Sega were more arcade experience driven; especially Sega. Nintendo did a great job bringing games like Zelda into 3D and it's my favorite Nintendo franchise because of how well it transitioned. It took until Dreamcast for the likes of Shenmue, Skies of Arcadia and other narrative driven games for them.
As for my personal history, I would have definitely had a Saturn (went with Playstation between the two). I would have still bought the Dreamcast at launch (probably). Depending on where I was at, I may have gotten the Dreamcast successor, but had Sega not jumped into narrative driven games the way Sony did with its first party devs, I would probably have grown passed gaming during the Dreamcast era.
The worst part of all this is.... Uncharted wouldn't exist.