Undertale! Even though I haven’t actually played this, I watched a Let’s Play of it (courtesy of Steam Train, have a look!) and got really into it. I love the different ending possibilities and the characters were amazing. I really wish I had played it myself rather than watch it though because now I know what happens and if I play it myself the effect will be spoiled. I don’t want to say a lot about it in case I ruin any plot but trust me, it’s really, really good.
Honourable mentions: Gone Home, Silent Hill 2, Bioshock
Dragon's Tea Party 
That certainly is a solid choice; not only is Undertale well-written, it flies in the face of other story-heavy titles by unapologetically being a video game. Contrary to what is commonly believed, it’s a superior effort to its peers because of that fact, not despite it. It’s too bad you haven’t played it; I highly recommend doing so.
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I will play it sometime in the future when I’ve forgotten enough about what happens!
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