Right, but why do you want to get to the end of the map? To see the next one, which hopefully has new monsters to shoot.
The story fits with this. Basically, you’re a marine (no name) dropped on a Martian moon to secure a facility. His team is wiped out, so he goes in alone. The facility is apparently working on teleportation, so he battles demons through the facility and into hell. After that, a portal to Earth opens and he enters to fight more demons.
Some notes here:
the Marine is never given a name, and you are never asked to provide one
the goal is to get revenge, not to grow as a person or defeat some evil (though you end up doing that)
there are no character classes, only weapons you find along the way
The character itself is completely forgettable, and there’s certainly no progression (you even lose all your weapons at one point). The game seems to go out of its way to distance itself from other games.
In an RPG, the character matters more than pretty much anything else. In Doom, I’m not given any reason to care about the character. Why am I doing all this? Because there’s baddies to shoot! That’s really all there is to it.
If it were an RPG, it would have some kind of persistent progression (levels, abilities, customized equipment, etc), as probably some kind of internal motivation for the main character (aside from simple revenge).