PlayStation owners don't have an exclusive game mode in Modern Warfare 2
But they do get an XP boost.
Call of Duty: Modern Warfare 2 does not have an exclusive game mode for PlayStation owners, in contrast to the last game in the series.
As part of Sony's agreement with Activision, Call of Duty games since 2015 had exclusive content for PlayStation owners, including game modes.
Call of Duty: Modern Warfare (2019) had a timed exclusive survival mode in Spec Ops, while Call of Duty: Black Ops Cold War had an exclusive Zombies mode called Onslaught.
PlayStation owners do, however, get some other smaller advantages.
The most notable one is space for two additional loadout slots in multiplayer. Players will also get exclusive double XP events and a 25% weapon XP bonus when playing with a party.
There are also exclusive cosmetic packs for PlayStation Plus subscribers and tier skips for the Battle Pass.
While this exclusivity agreement between Activision and Sony has existed for several years, it has recently become contentious thanks to the proposed acquisition of Activision Blizzard by Microsoft.
But it should be noted that prior to the existing agreement, it was Microsoft that had an agreement with Activision to bring exclusive content to Xbox first. Indeed, in the Xbox 360 generation, players would receive DLC maps an entire month before other platforms.
You can find a full list of PlayStation exclusive features here.