The upcoming Doom 4 beta will only be available on next-gen consoles and PCs.
Wolfenstein fans, very broadly speaking, are generally likely to be Doom fans too, so access to the Doom 4 beta (whenever it may happen) is a nice little bonus for preordering Wolfenstein: The New Order. Unfortunately, while everyone who preorders will be invited to the party, not everyone will actually be allowed in the door.
"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. All PC purchases will receive an invite to the PC Doom beta," the FAQ states. "The Doom Beta will only be available on Xbox One, PlayStation 4, and PC."
Doom 4 is being developed for the 360 and PS3, so why the restriction? Your guess is as good as mine, but with no launch date announced its possible that those versions may lag behind the next-gen and PC releases; it's also possible, and probably more likely, that those versions are "better" than the previous-gen editions and Bethesda just wants to put its best foot forward when it unleashes the game on a public audience.
Either way, consider yourself warned: If you don't have a hot new console or a decent gaming PC, that Doom 4 beta invite you've been looking forward to isn't going to do you a whole lot of good.
Source: Doom 4 Beta FAQ