You can do it in 5e too. For instance we have death at 0 and no cleric or any access to resurrection magic in our game. Death is a real threat even into high tiers (lvl 15 now). If you use things like lingering wounds (DMG variant) or liberal use of exhaustion, you can dial up the horror mechanics pretty quick. In fact, we had to stop using lingering wounds because combat became to horrifying for my players!2. Mechanics. If you use older editions, there are mechanics (such as aging, level drain, insta-death, and so on) that are legitimately terrifying; these mechanics, or even the thread of these mechanics, can make the game much scarier.
You appear to be confusing "Alien" with "Aliens." Aliens had the soldiers and was not a horror movie. There are no soldier's in Alien and it is a horror movie.It's funny that Alien was brought up as a horror movie because I think of it more as a creature feature.
But anyway, was Aliens a horror movie? I mean, everybody but Ripley sent to the planet (well and token idiot management guy) were trained soldiers at least theoretically well suited to the task.
I think it just upped the ante by showing that even the well trained marines were chewed up by the enemy. It took more enemies than in the first movie, but the result was the same.
3) Their are variants for recovery and lingering wounds in the DMG, and using a houserule (like we do, 0 hp = death) doesn't mean your not playing D&D.3. No lasting damage. Long rest instant restore.
4. Easy removal of conditions. You got the gold the FNC (Friendly neighborhood Cleric) has a spell for that.
You appear to be confusing "Alien" with "Aliens." Aliens had the soldiers and was not a horror movie. There are no soldier's in Alien and it is a horror movie.
Why would they both need to be horror movies? But, no, Aliens is not a horror movie. Alien (no s) is definitely a horror movie.Well that was the question - if Alien is considered a horror movie is Aliens also considered horror movie? Personally I'm not sure I'd qualify either one as a horror movie, because not all monster movies are horror movies. But if you classify it as a creature feature then I think both fit the bill.
But, we're talking games here not movies. I think D&D absolutely can have most of the features of many of the horror genres, whether it can be a horror game is open to interpretation. Kind of like how "who would win in a fight between Batman and Superman" the real answer is "depends on who you ask".
Why would they both need to be horror movies? But, no, Aliens is not a horror movie. Alien (no s) is definitely a horror movie.
Aliens IS a horror movie. It’s also an action movie. But everything from Ripley’s nightmares, to Weyland-Yutani’s nefarious plan(s), to Newt’s capture and rescue are squarely horror.Why would they both need to be horror movies? But, no, Aliens is not a horror movie. Alien (no s) is definitely a horror movie.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.