[Update: According to Microsoft, this problem falls entirely on Activision. Microsoft allows the possibility of cross-play with UWP apps and CD Projekt Red's upcoming GWENT even has the feature. I'm guessing Activision just wants the game on as many platforms as possible, though limiting such a crucial feature of Call of Duty makes little sense. The original story is contained below.]
In some not so shocking news, the Windows Store version of Call of Duty: Infinite Warfare will not support cross-play between the Steam (or retail) version of the game. This also affects Modern Warfare Remastered, which I'm surprised to learn is even hitting the digital store.
I'm not sure what Microsoft's long term goals are for the Windows Store, but not allowing play between the same hardware is a bizarre choice. At the very least, since UWP is an Xbox platform, allow play between Xbox One and PC; that is also not supported, though (the game is not an Xbox Play Anywhere title).
I feel sorry for anyone who decides to buy this version of the game. I doubt that performance will be poor (though past Call of Duty PC ports have been shoddy), but no one is going to be playing these versions. Getting to the top of the leaderboards should be a breeze for the five people who end up with these versions.