Is Black Ops 3 cross-platform

Er, we'd need more details than that. Your GPU, for a start. Run "dxdiag" and append a log output from that to your answer. You will have this installed on Windows already, because it comes with DirectX. A screenshot would also really help because depth-of-field is commonly used in this game, and it could be a result of that, but I'd have no way of knowing unless I saw the visual effect myself.

Until then, try turning off depth-of-field in the graphics settings if the game allows it. Also keep in mind that this game hasn't actually been released yet.

It appears that if you buy the Season pass (available on steam), it comes with "The Giant" zombie map. From the link:

 About This Content
 The Call of Duty®: Black Ops III Season Pass delivers 4 epic DLC map packs
 in 2016 with all-new multiplayer content, including re-imagined 
 fan-favorite maps from Call of Duty®: World at War and the Call of Duty®: 
 Black Ops series, plus thrilling Treyarch Zombies content, all for one 
 great price.*

 Fans that order the Season Pass will be among the first to experience
 the return of Zombies with “The Giant” Map in all of its undead glory
 on Day One. Set in a World War II-era research facility featuring the
 weapon-upgrading Pack-a-Punch Machine, re-live the chaos of Treyarch's
 classic "Der Riese" Zombies map, picking up the Zombies story with
 Dempsey, Nikolai, Richtofen, and Takeo where Origins left off.

Purchasing the Deluxe edition also gives it to you (since it comes with the season pass).