Lately I've noticed an increase in the amount of discussion surrounding the use of the term "Roguelike" and how it should be applied to games. Now, I've been aware of the Roguelike scene for approximately four years now (small fry compared to some, I know) and the topic of the name of the genre itself is something that comes up arguably too often. It is, at its core, an entirely semantic discussion and not necessarily one worth having - certainly not one worth alienating people over. Still, to completely ignore that, let's go over it real quick.
First off, a Roguelike in the strictest of senses is a game that is like Rogue. To go even deeper, Rogue is a dungeon crawler and a dungeon crawler is essentially a focused role-playing game. I like to describe Rogue (and roguelikes) as stripped down RPGs and I mean that in the best way possible. They typically forgo elements such as a gripping story or immense graphical fidelity and instead focus on gameplay mechanics. This is almost certainly the main reason that Roguelikes are pretty common amongst hobbyist game developers. You can make a traditional Roguelike and essentially just worry about programming. Still not a small task, but definitely simpler than programming plus art assets plus music plus writing. Anyways, it's generally pretty easy to spot these traditional Roguelikes. ADOM, NetHack, Angband, and Dungeon Crawl, along with many more, are all fairly straightforward in the sense that they are definitely Roguelikes and you'd be hard pressed to find someone who disagrees.
Once you start to look past the traditional Roguelikes things start to get muddy fast and people disagree heavily on what "counts" as a Roguelike and what doesn't. Some will compromise and try to use terms such as "Roguelikelike" or "Roguelite", though I personally am not a huge fan of either term. The term "Roguelike" is already pushing the border of clunkiness, no need to stretch it further. The controversy here seems to be from certain games such as the Binding of Isaac, Spelunky, Rogue Legacy, and FTL using the term Roguelike or having it associated them without literally being a traditional Roguelike. Is it wrong that games with Roguelike elements use the term even though they aren't literally ASCII turn-based dungeon crawlers?
If we look at the mechanics surrounding a typical Roguelike, I think we can conclude that it was inevitable for more and more games to eventually pick up on Roguelike elements. As mentioned, Roguelikes tend to forgo aesthetics and focus heavily on mechanical depth. Without strong mechanics, a traditional Roguelike has nothing - so developers try to create that out of both necessity and tradition. Roguelikes, in a lot of ways, were ahead of their time - some types of AI design and procedural generation first gained real traction in the Roguelike sphere. These types of mechanics are not things that are uniquely desirable to Roguelikes - being able to generate a world with an interesting ruleset is something that could be interesting in basically any genre. For example, the Binding of Isaac can be seen as a top-down shooter incarnation of Roguelike mechanics and Spelunky can be seen as a platformer incarnation of those same mechanics.
Basically, I'm not convinced that using Roguelike as an adjective like some of the aforementioned games do is a terrible thing. While they aren't strictly Roguelikes as according to the Berlin Interpretation, I don't believe that is such a terrible sin that we as a community should excommunicate all games that don't meet a rather strict definition. These games definitely share in Roguelike design, at least in a mechanical sense, and that's something that can benefit Roguelikes as a whole. In conclusion, try not to let your world be rocked by genre names and how they're used - at the best of times they're opaque descriptors, at the worst of times they strangle design and send fans into a frenzy.