We've run into this problem quite a few times with our work at Tale of Tales. Even when we remove all gameplay, gamers are still inclined to rush through in an attempt to "beat the game". They don't seem to realize that the experience is about the walking itself and not about the goal you're walking towards. We haven't really found a way to direct this properly.
Collecting the flowers in The Path was sort of an ironic gesture to illustrate how playing The Path as a game was pointless. But it was also a system to lead players deeper into the forest. Not all players appreciated this. But the discussions between players who did and those who didn't often worked as a self-help therapy.
We tend to put a lot of effort into slowing players down, in an attempt to force them to savour the moment. But that doesn't always work either. They often start complaining about "bad controls" when we don't allow them to efficiently get from point A to point B, etc.
In my experience, females are a lot better at this than males! Women and girls tend to investigate a lot more and observe and interpret things more actively. In general, they are a much more grateful audience, I think. So how do we teach boys how to play like girls?
When we send review copies of our games to journalists, we often accompany them with some warning in the message: "don't play this as a game, take your time, stop playing and think about the game, if you force the game you won't enjoy it", etc. This does seem to work. So maybe this can be done with players too? Gamers may often
act stupid but they are often quite intelligent. Maybe if you just tell them ahead of time that they should take in the moment-to-moment experience instead of trying to "beat the game"?
Horror games are kind of easier than others because you can do a lot of illogical things and it just adds to the narrative of fear. You could simply remove items from the inventory after some time, e.g. so they are forced to use the items or lose them. Or you could increase their score/reward if they take their time in a level (though this would only affect people who play for points).
It's a big problem when addressing the gamers audience. I hope some other people have some good ideas about this.