While those who have pre-ordered or bought the game, you guys are guaranteed a spot in the closed beta, but the alpha will be limited so even if you did, it’s not a guarantee that you will be able to get in. The alpha itself will also be limited in terms of what gamers can expect. As the name implies, it is an alpha so it will probably be very different from the finished product.
Also as Bethesda notes, “The DOOM MP Closed Alpha is a series of development-driven tests designed to stress test the game’s dedicated server infrastructure in a real-world consumer environment. It is not the Beta (offered with Wolfenstein: The New Order pre-order), a demo, or representative of the final game.”
Other limitations include only giving players one map to try out, one mode which is 6v6 team deathmatch, one demon to face, one power weapon to try, and 6 regular weapons with 2 equipment items. To sign up, head on over to Doom’s website for the details.