I know it's just an multiplayer arena shooter compared to other Quakes, but it's really creepy. I feel like I'm in Hell-like environment when I see videos of this game.

Is this game a horror game?

Do you mean to tell us that you are scared when you play quake3?

no it's not.

It's a competetive shooter. No scare elements, no horror elements, no story except: go into an arena and dominate over competitors

No. Quake could be considered a horror game, Quake 2 is just more of a standard apocalyptic sci-fi shooter. Quake 3 just takes design influences from the previous games.

There's no horror element because there's no real storyline.

Of course it's nothing more than a competitive shooter, but still it's full of death metal theming and satanic symbolism.

Yeah it gets pretty scary when you're going 35-1 and doomguy pops outta nowhere with a railgun

There is no Satanic symbolism, only the symbols of our Lord and Savior Jesus Christ. The pentagram is a symbol of the five wounds Christ received while dying for your sins, so every pentagram is a reminder of Christ's love! It's a game all about love!

Pussy

But only as long as one point is projecting upward.

If it's reversed, things are going 180 degrees upward. And map designers intentionally put these pentagrams so it appears reversed most of the time.

"A reversed pentagram, with two points projecting upwards, is a symbol of evil and attracts sinister forces because it overturns the proper order of things and demonstrates the triumph of matter over spirit. It is the goat of lust attacking the heavens with its horns, a sign execrated by initiates." - Éliphas Lévi

So Quake 3 is a horror competitive FPS game, right?

It's full of Satanic symbolism, guy... Guess how popular would Counter-Strike be if it was splattered with hellish/Satanic design literally everywhere.

The only one I've seen was on the floor, which means you can point it any way you want!

Some are on a ceiling, most of which are purposely built to appear Satanic too.

Most of them are pentacles, and most of those are satanic, too.

There are goat heads, skulls, inverted pentagrams pretty much all over the map.

To answer your question, no, I wouldn't consider Quake a "horror" game. Perhaps the art style leans a little towards a horror aesthetic, but I'd say it's more of a gritty fantasy. I have played the game since it's inception 20 years ago, and noone who I have ever talked to in those 20 years has ever classified the game as "horror".

At least it's not a survival horror, because you always respawn after you die, right?

Wolfenstein 3D is one big exception.