This is Reflex. Reflex is a modern homage to the old Arena FPS's, taking particular inspiration from the CPMA mod of Quake 3. This isn't the same game, as there are many new movement options previously unseen in other Quake games or even other Arena FPS's in general.
From the game's Steam page:
"Reflex is a competitive Arena FPS that combines modern tech with the speed, precision and freedom of a 90s shooter. If you sunk countless hours into the Quake or Unreal series, Reflex will feel like a welcome return of the old school shooter feel."
The game is still in Early Access, but has added many features such as
- custom HUD and visual widgets
- Steam Workshop integration
- integrated and supported Community Maps
- Armor and Melee weapon customization
with more coming up. This game as of 1/11/17 has just gone to Version 0.48, so there is still much to go before this game is completely finished. However, I strongly recommend this game to all diehard Quakers, and I hope to see y'all in the arena sometime.
For those needing some help getting started, these are some great resources to understand what you're getting into: