I've noticed a common theme with games that I can pick up and play 15 or 20 years after release and still feel deserve a 5/5 score; they're almost always an evolutionary step in a well-established genre, rather than a genre pioneer. Sometimes it's the evolutionary apex of a genre, and it's all downhill from there. Once the freshness of a new concept wears off and the cutting-edge graphics become dated, all you're usually left with is janky play control and some shortsighted design decisions.
Doom 2 falls in sort of an odd middle ground between those two points. It's an evolutionary step, but its predecessor was the first major step forward from the first real effort in the FPS genre, and Doom 2 itself is really just Doom warmed over with new levels and a handful of very minor tweaks to the original engine.
Being so far back on the FPS evolutionary chain, Doom and Doom 2 thus suffer to a great degree from datedness; on modern high-res displays, the simple flat textures and stiff chunky sprites look a bit silly, and you can't even get the now-standard WASD/mouse control unless you patch it in (or use a Doom source port like Freedoom or Vavoom.) You're also dealing with Romero's antiquated philosophy of level design, which basically boils down to "teleport monsters in behind the player whenever they push a switch and hide snipers on high ledges constantly."
I said about the first Doom that it passed my "desert island" test, though; if I was somehow stuck on a desert island with that as my only game, I could probably play it contentedly for quite awhile as opposed to, say, staring at sand or getting oral from a volleyball. This being fundamentally the same game, I guess it does too. Doom was far from the evolutionary apex of the FPS genre; its simple action-heavy strafey-shooty style would be eventually surpassed by Quake, Serious Sam and Painkiller, and that's not even mentioning the multiple branches that would spring out - RPG elements and horror in System Shock 2, complex mission objectives and splitscreen multiplayer in Goldeneye and Perfect Dark, stealth in Thief and Deus Ex, tactical squad combat in Rainbow Six and Counter-Strike, and massive online multiplayer in Battlefield 1942 and Team Fortress. You can certainly argue that the FPS genre has apexed and is now sliding downhill into increasingly linear, on-rails glitzy jingoist spectacle (and I won't argue against that notion), but that tipping point wouldn't occur until at least a solid decade after Doom 2 was released. So you've got a lot of material out there that's similar to Doom 2, but simply better; it gives you everything Doom 2 can give you, but also a lot more. However, Doom 2 is still solidly made, entertaining, and has all sorts of modding and multiplayer possibilities.
5/5s here aren't automatically given to games that were at one time the biggest thing in gaming or moved an amazing amount of copy; they're reserved for games that have almost entirely held up over time, and will still be as much of a blast to play 20 years from now as they are now. Doom 2 doesn't entirely land in that camp, but it's close enough for a 4.