I start :

#1 The weapons:
What can i say ? I LOVE the simplicity and the way the quake weapons work. You have top tier weapons, and the rest. It just work wonderfully. Long range: rail; med range: lg; close range: rl, as simple as that but yet insanely hard to master. Once you understand how the weapons work it's pure joy to play quake really. The weapons are so well designed and fun to play, as well as very balanced which makes it a very unique experience.
Also, no gimmicks, the weapons are simple and no alternate fire or some other gimmicks bullshit.
And players are building their playstyles around the weapons, which is the true beauty of quake.
And ofc when you use a weapon it feels very satisfying, i mean, the feeling of the weapons is unmatched.

#2 The movements:
Quake without strafe-jumping or bunny-hopping or both, isn't quake. Defrag runs and trickjumps movies are VERY impressive to watch and doing them as well as moving through the maps is very enjoyable. Pretty simple movements mechanics, but still VERY hard to master, which makes players like w3sp, dex, v3rb or walter look very unique. I have a lot of respect for these movements masters.

#3 The content:
Duel, TDM, CTF, instagib, freezetag, CA, defrag and some less popular gametypes but still fun like Domination, and the ammount of different maps to play, everyone can find something he loves. Yes, the community is probably a little bit too much splitted, but let's be honest, if you play quakeworld or quake 2 or warsow or reflex or quakelive, whatever, you're still considered a quaker in my eyes :). Whatever gametype you play, whatever quake you play, you're still a quaker :). Unlike games like CS:GO where there's basically only 1 gametype and like 5-7 maps played.
Quake is huge in that regard comparing to most others fps.

#4 The community:
Guys, you can't imagine how much i love you all. Esreality is the best gaming website i know, I load it up everyday each time i start my computer. It's full or trolls, attention whores, retards, everyday normal guys, very honest and serious guys, some geniuses, good contributors to the community, hardcore quake players, funny guys, and so on. It has everything you need to entertain you really. And i didn't even mention the charisma of most of the pros quake players.

#5 The deepness of the gameplay:
Out of all the multiplayer games I played my whole life, Quake is probably the deepest, gameplay-wise. Like i said above, it's simple to understand, but so so hard to master. You can spend your whole life playing bloodrun or thunderstruck only and you will still always have rooms to improve. It's endless.
It's so amazing to see players like evil or k1llsen play bloodrun in 2016, and compare it to the early days of this map. The overall skill of the pros has so much improved throughout all these years, it's beautiful, just beautiful.
The only game i can think of, that can somewhat compare to quake concerning its skill-celling, is starcraft. Really it's the only game. Quake is unique :).