Sadly the only people who are able to be in this closed alpha are those who purchased Wolfenstein: The New Order and signed up for access.

Hope is not all lost, though: beta is supposed to take place early next year if Bethesda keeps their word. We can assume like with all games there is usually a closed beta then open beta, but surly they will continue to promote Wolfenstein: The New Order during these tests as well. It seems to be a pattern right now.

If you are outside of the US and are having troubles finding out if you are eligible for the closed alpha Bethesda does have instructions on their Twitter that may help you. 

The alpha test is limited in its content since there is only a single map and one game mode available (12-player team death match), and only seven weapons available. Along with the limited content is the lovely non-disclosure agreement which tries to prevent players from sharing anything about the game. We all know that doesn’t stop some people though.