Here's a counter-question: why should we regard Story and Gameplay as separate?

Games tell stories all the time, even the games that you mentioned as more 'gameplay'-oriented. The difference is that the games that usually fall under the 'story-oriented'-category, are crafted by the game creators, while the other is purely player-driven.

In Binding of Isaac for example, you could tell about your last great run: "Dude you don't believe WHAT just happened!". Or you could tell about the great assault that happened in the last Battlefield map you just played.

DayZ is another prime-example of player-driven storytelling, with hundreds of players interacting with each other. This has resulted in some very interesting moments (you can check some of these on YouTube), which currently cannot be done with story-driven games and AI (in my opinion).

Now here's where it gets difficult: can these gameplay-oriented stories convey more than your usual encounters with other players? Moments that actually amount to a good story are rare and usually don't really amount to much deep pondering (like you would have with deep philosophical games like the Deus Ex or Metal Gear franchise). This is because the primary author is the player: there's no pacing nor foreshadowing happening in a live gameplay segment.

Telling a story through cutscenes is not the ideal way either. Sure using them isn't wrong, but when a game primarily uses them for storytelling, something tells me that this would probably worked better as a movie.

So to come back to your question, I believe that the best games are those that combine the story and the gameplay (or interaction if you will) so that they work in synergy. A good example is Papers Please which is a combination of player-driven decision making, but it also has a fixed amount of endings: it's the combination of two. Two other good examples are Journey and This War of Mine.

So gameplay can be actually used to heighten the game's story and themes.

This is primarily the reason why I think Last Of Us works well: it builds the relationship between Joel and Ellie not only through cutscenes but also through gameplay. Ellie starts to grow on you, when you spend something like 10+ hours with her. This sort of thing is hard to do with a two hour movie or even a television series! The game also uses the gameplay to heighten the theme of survival: throughout the game you try to scavenge and craft items for survival. What if this feature wasn't in the game? I believe that it would take a big part out of the experience.

So to sum it up (or TL;DR): Gameplay and stories might be seen as separate things, but they really should be desinged to work in synergy and to heighten the experience. Games can tell stories through multiple ways and we are constantly discovering new ways to immerse and affect players.

Just like the movie industry developed new cinematic techniques over time, so will the game industry develop new ways to affect the player with interactivity.