That's the difference between soft interactivity and hard interactivity. The type of interactivity I'm talking about is in some sense literally altering something, not perceiving it differently. For example, I'm not simply perceiving Mass Effect 3 differently if I shoot a certain scientist in the mid-game (we probably all know to whom I refer), I'm actually experiencing something different than if I had not shot him.
That's certainly true, but I think this approach becomes overly literal, especially with more story-focused mediums: films and novels for example aren't being perceived when they're sitting on our shelves, outside their front covers. On the other hand, we have a whole host of performance art (including music) too that literally can't be perceived when not in practice. As a side point, the interactivity we have is often too viewed as an implementation of the artist.
As an example, when ME3 came out, we had reviewers come out and say that they were against changing the ending on artistic integrity. Fans pointed out that ME was essentially a choose your own adventure book, but they countered that technically-speaking every decision was Bioware's, not ours, even in that context. In effect, every decision we are given was the creative decision of an artist, in some capacity. Bioware may have given us a number of different ways to interact with Garrus Vakarian, as an example (more than we typically associate with other mediums), but even in the context of not talking to him all, pushing him paragon, or pushing him renegade, we had some artist involved laying out the dialogue for Garrus, the dialogue for Shepard, and how he feels the scenario should play out. The sheer amount of artistic control in terms of writing characters, setting, and the overall narrative makes the chess comparison a bit more difficult.
So we're left to make up our own conclusions on if we think things are handled well, or not. And I respect alternate conclusions, as long as they don't claim to be objectively true when they're not. If people think these things are handled well, that's fine, but I just do not agree.
To be clear, I don't recall that being pushed as the objective truth (will double check). It was put out as being an option which the creator could view as making for an improved experience. In describing naked fine sculpting, the point was not necessarily to illustrate that all naked sculpting is objectively better, but to illustrate that there is an entire artistic medium where it's looked on as a positive. It's meant to provide credence to the idea that it's a legitimate option for an artist.
In other words, I think there's a difference between saying "but what's the point of making them naked?", which is why people point out a long-standing/highly respected practice, and saying "Aristic integrity be damned, I don't want naked people in my games". I generally fall into the latter camp.
As a side point, just given the general depiction of naked characters in video games, I wouldn't disagree though that (thus far) it's been done for pretty weak reasons.
I'd still classify Bioware as closer to a board game because of the fact that their games aren't merely interpreted, but are in some sense shaped by, their players. It's about your choice (at least insofar as their standout qualities). Further, it's interactive in the strong sense as opposed to the soft sense. Meaning, while art is interactive in the sense of you may be moved to interpret or feel a certain way about it, you do not actually interact with it. In Bioware games, however, you do shape much of what occurs and no 2 stories are the same (generally). Strong vs soft in this case would altering a painting vs observing a painting, respectively.
I hit on this a bit above, but I'm not sure how much benefit we get from the distinction, going back to traditionally story-focused media. With a book, the words might exist, but the medium is inherently more subjective since the story can only call so many details to the mind's eye, at which point the viewer makes up the rest. Likewise, the book sitting on our shelf or the movie we watch isn't really doing anything, until we interact with it, at which point our interpretive approach takes hold.
Putting that aside too, we run into issues like the Halo example, which does go out of its way to render aesthetically amazing cut-scenes, which are within the full control of the writer. As a player, you have two options: watch the cut-scene or don't. And in Bioware's case, they make a substantially greater effort at implementing companion characters with story arcs, designing the general world, and providing plot points for players.
I think, for what you're suggesting to apply, the developers would have to feel little to no control over the story/experience they're shaping and I'm not sure how well that works even in the context of Bioware games. Even going back to your Mordin example, some writer put together the overall arching plot on who Mordin was, how he felt regarding certain matters, how he would respond to Shepard's inputs, as well as how his story could potentially conclude.