"Strafe jumping is an exploitable bug. Just because people have practiced hard to allow themselves to take advantage of it does not justify it's existance. When I tried fixing the code so that it just didn't work, I thought it changed the normal running movement in an unfortunate way." - Carmack
If you're curious to see some gameplay from 2016, there was an "all-star" 4on4 competition recently, on YouTube with commentary here: https://www.youtube.com/watch?v=oN6s1nh6nV0
It might look different to the Quake you remember — after id open-sourced it, some really great community projects sprouted up improving both the clients and servers, but the gameplay stays exactly the same.