The Realm of Shadows may be the same World of Shadows as the one that becomes visible when a [Elixir of Shadows] is consumed. It may also have something to do with shadow magic and shades. Death knights, necromancers, and undead as a whole share a strong connection with the Realm of Shadows from many hints that can be seen in-game. In the death knight starting zone, death knights are given the task to enter the Realm of Shadows in order to gain their Deathcharger. Later on, death knights are eventually able to learn the ability [Raise Ally] which pulls their ally's spirit back from the Realm of the Dead and forces it back into their body. Upon doing so, a buff is applied to the player stating that: "A touch of the spirit realm still lingers..." This shows that death knights and necromancers both have a connection to the Realm of the Shadows/Dead to perform necromancy which furthers the idea that they actually are drawing their magical power from it.
It's hard to get a sense of an entire World of Warcraft expansion from 30 minutes of play. In my short demo, I recreated my main (a Beast Mastery Hunter) and played through the introductory quests from the Bastion zone, a heaven-like plane from Azeroth's afterlife. The minute-to-minute gameplay very much followed the formula of modern WoW questing, with a variety of tasks like challenging specific enemies to duels, helping craft things in timed minigames, and of course, killing 10 rats (well, not rats, but they might as well be).
Frankly, the aspect of Shadowlands I'm most excited about is an overhaul of the leveling system—something that wasn't a part of this demo in a major way. This kind of breaks the rules of a hands-on article, but I want to take an opportunity to talk about it and why I think it's interesting, regardless, since it came up in my interview with WoW developers.
During the Burning Legion's third invasion, the Knights of the Ebon Blade traveled to the Shadowlands to acquire the Aggregates of Anguish, five tormented essences of powerful souls - Admiral Proudmoore, Soulbinder Nyami, Grand Empress Shek'zeer, Grand Apothecary Putress and Archmage Arugal. Salanaar required these to conjure the Steeds of the Damned for the order's new Horsemen.