I don't know, I think that there is enough of a story. It is a short game, after all. Maybe it's because I usually play the types of games whare the story slowly unfolds as you work through the game, rather than it being in your face, so to speak.
One of the first things I did in Day 2 was click on the pool, so I had a strong directive to try and empty it. Phil also made a comment about finding some pipes with the metal detector, so that planted the seed about what needed to be done.
I'm definitely curious about the portrait changing, and the way people disappear. As usual, I like to conjecture about things:
Spoiler:That statue in the trophy room, I'm sure it's cursed. I'm thinking along the lines of Shivers.