It wasn’t the first first-person shooter, not quite, but it was one of the first for PCs, and it’s unquestionably the one that blew the genre wide open.
Doom is fantastically primitive by today’s standards — even though you’re moving through a nominally 3D space, you can only move and shoot in two dimensions.
But at the time the gameplay experience was overwhelmingly immersive and addictive, thanks to the programming genius of John Carmack, who authored the physics engine — and it established the look and feel of later shooters as surely as Xerox PARC established the rules of the virtual desktop.
Its impact also owes a lot to the gonzo horror sensibility of its designers, including John Romero, who showed a bracing lack of restraint in their deployment of gore and Satanic iconography; id gambled by releasing the first third of the game as shareware, and their gamble paid off hugely. Demand surged, crushing servers worldwide, and Doom rapidly became ubiquitous. It also featured user-modifiable maps and graphics in the form of WAD files, and the swapping and modding of Doom WADs gave rise to a large and robust online community.