Doom 3 is a fantastic game on its own merits and doesn't get enough credits for its accomplishments. It's been 20 years since it's initial release, and at the time it was truly cutting edge with a level of fidelity we had never seen before.
ID Tech 4 delivered an incredible engine with capabilities such as real-time lighting and shadows, detailed bump mapping, interactive GUIs, powerful scripting, animation & sound-systems and so much more. Add to that a very large amount of geometric detail and texture variation compared to other games at the time.
The game took a much more dark and grounded approach to concept, which was extremely refreshing for many people coming out of the 90s. It wasn't going to have characters running around at 1000 miles per hour as it was going for something way more immersive, atmospheric and realistic as stated early on by mr.Carmack himself.
Story wise, despite what some might say, it's not in the way very much at all, and in fact for the most part everything is optional with the excellent implementation of the PDA-system which gives you the choice of how much you care. The fact that the game has about 20 minutes of intro was necessary to make the world feel believable, rather than just dump spawning you into hell and acting like it's 1993 which would've felt off given the direction and buildup of the game.
Gameplay wise, the play between light and dark is really the core pillar a long with the smooth methodical gameplay that really brings the immersion on top. The tension that builds from you having to trade firepower for visibility works extremely well with the dark design of the game, and also benefitted the performance of the game at the time. This is also why many people who enjoyed Doom 3 for what it was didn't appreciate the BFG-edition that threw that under the buss just to cater to those who wanted D1,D2 in D3.
Another somewhat controversial topic was the shotgun and the fact that it wasn't "effective enough". Well, this is simply game balancing, the D3 shotgun absolutely shreds even late game enemies by just a shot or two, but it requires you to shove the gun down their throats as a risk reward tradeoff. Tinkering with this just makes so many chess-pieces come out of balance in the entire game, instead I enjoyed it for what it was intended to do.
It's a shame that the ID Software of today seems so afraid of upsetting the butt hurt mob of anti-d3ers that they barely mention the game on its 20th anniversary. A bunch of people who to this day just can't accept that the game just isn't for them, rather than acting childish.
If you want to play the game today I'd heavily recommend running the source-port dhewm3.org that has a ton of bug fixes, widescreen support and generally just makes the game run without hassle on modern systems while staying true to the core experience.
If you're feeling spicy there is a mod or two I'd recommend, throw the alpha-sound in for the pistol as It makes a world of difference as well as a texture-pack such as the Wulfen-textures which adds a ton of more detailed and renewed textures. Couple that with sickmod, and you've got a fantastic looking game even by todays standards which is a testament to all the hard work that went into it.