The definition of roguelike as a genre has been a subject of dispute since it became a thing after the original Rogue back in 1980. The Unix game used ASCII graphics to represent its game world, featuring randomly generated environments, permadeath, and tile/turn-based gameplay. The International Roguelike Development Conference 2008 gave a rigid description of what constitutes a roguelike, including "rooms connected by corridors", which was how the dungeons in the original Rogue were laid out. Modern roguelikes are taking a fresh look at what is possible in the roguelike space but are being ostricised because of it. According to hardcore Roguelikers, their games cannot be roguelikes because they do not meet these strict specifications. New roguelikes are being called Roguelike-likes or Roguelites, in order to distinguish themselves from a genre that has been nearly dead for several decades.
So how do we define a roguelike? The most important thing to do is figure out what a roguelike is actually about. The point of the random generation is to provide a new and different experience every time you start the game and the permadeath makes your actions and choices matter, rather than restart to the nearest checkpoint whenever anything goes wrong. You must now take risks and live with the consequences. Because everything isn't perfect, you can generate interesting stories. You aren't just winning or losing, you're somewhere in between. You can be be in peril, in situations where you might die but can still survive if you play smart. This is where the heart of the gameplay is and where emergent stories can happen. That makes roguelikes different and compelling, and really defines the genre.
Let's be realistic; these new roguelikes are here to stay. They are the natural evolution of the genre they were inspired by, and to be rigid about the definition of a genre is to limit what that genre is capable of achieving. Like most words in the English language, the meaning of roguelike has evolved over time. As an example, modern Cappuccinos are massive, foamy affairs, but the Traditional Cappuccino is rather small and is more balanced. I recommend we use a similar naming scheme here: "Roguelike" for the newfangled randomizers and permadeathers like FTL and The Binding of Isaac, and "Traditional Roguelike" for the turn-based RPGs like Dungeons of Dredmor. That way, no one gets excluded from the roguelike table and the genre can continue to evolve without fights over the name.