A beta for the game formerly known as Doom 4 is included with pre-orders of Wolfenstein: The New Order. And while MachineGames' shooter is cross-gen, the Doom beta will not. Bethesda has confirmed that the beta will only be available on PS4, Xbox One, and PC.
"DOOM beta access correlates to your pre-ordered Wolfenstein: The New Order platform," Bethesda told Gamespot. "If you purchase an Xbox 360 or Xbox One version of Wolfenstein: The New Order, you will receive an invitation to the Xbox One Doom beta. PlayStation 3 or PlayStation 4 purchasers will receive an invite to the PS4 Doom beta." And while the Xbox One beta will require Live Gold, the PS4 beta will not require PlayStation Plus.
The next-gen-only beta could suggest that the new Doom is targeting those consoles exclusively. However, given we've heard nothing about the game since its was mysteriously delayed, really anything is possible.