The Deluxe Edition is listed as a physical release; product details and the item description both identify it as the physical version.
You experience the story from both Alan Wake's and Saga Anderson's perspectives—the game presents events through each character's point of view.
The Deluxe Edition is single-player only. Product details list Number of Players as 1 and note that multiplayer is not supported.
The Deluxe Edition includes Alan Wake Remastered (Digital Edition) as a gift-with-purchase DLC delivered on a voucher.
Included cosmetics are: Nordic Shotgun Skin and Crimson Windbreaker for Saga; Celebrity Suit and Parliament Shotgun Skin for Alan; and a Lantern Charm for Saga.