I love me some traditional roguelikes, but I'm also on board with the modern expanded usage.
The way I see it, the true essence of the genre is twofold:
-Both the resources available to the player and the challenges facing them are the result of complex interactions of systems with significant random influences.
-Consequences are permanent, with no "load game" safety net. "Permadeath" gets at this idea, but is too narrow for my taste, since so much of what I like about the genre is the weighing of possible consequences short of death.
There's nothing about these principles that tie them to any particular set of gameplay mechanics. Rogue itself and its immediate descendants applied them to a turn-based RPG base, which worked great. But this resulted in things like the Berlin definition fixating on the RPG mechanics (turn-based, dungeon crawling, item identification, inventory management, etc.).
So Rogue is a roguelike RPG, Spelunky is a roguelike platformer, Atom Zombie Smasher is a roguelike tower defense, etc.