The last we checked Quake's name/trademark was owned by id Software. Let's see and wait what will develop, in mean time watch the video below.
Read original game description from id Software site:
"Rage through 32 single player levels and 6 deathmatch levels of sheer terror and fully immersive sound and lighting. Arm yourself against the cannibalistic Ogre, fiendish Vore and indestructible Schambler using letal nails, fierce Thunderbolts and abominable Rocket and Grenade Launchers."