As above I'm looking for a really good game of each.
I've got strategy sorted in a say with Cities.
I want a death match game and large open world, ones that don't become obsolete quickly.
Deathmatch:
The genre has all but died, the closest you will get will be as you say quake champions atm.. Doom 2016 has a reasonably active multiplayer scene too, as i am sure Doom Eternal will be when it comes out later this year
Open world:
I'd honestly reccomend Rage 2, for me having 100%'d plenty of open world games such as Spiderman PS4, most of the AC games, Borderlands, Fallouts and Far crys.. Rage 2 is genuinley a great game, the open world is a completionists dream, the environment is interesting and on a decent PC the game is stunning. Not to mention it has the best gun mechanics of any game similar, on par with doom 2016 but with super-powers.