As a story, my father's long, long legs is original, weird (in the Lovecraftian sense of the term), and excellently scary. It is the kind of story I will need to mull over for a while, (Spoiler - click to show)especially given the lack of a conclusive ending. The writing occasionally feels a bit lacklustre, but when it is good, it is very good. The concept is excellent and uncanny.
As a Twine creation, I'm in two minds about it. Visually, it's very good. The grayscale background is a subtle, superb touch: representing the dwindling light falling into the father's basement; brightening or darkening depending on the events of the story. However, once the novelty wore off, I ended up feeling that the Twine format was a gimmick. The story is static; the vast majority of segments only have one link to click to get to the next one. The narration didn't even use the simple trick of second person to give the reader a sense of agency. I enjoyed the story, but I felt I would have enjoyed it equally if I'd read it in print or on a static web page.
(Spoiler - click to show)Then I got to the final section, and the story unleashed all Twine's possibilities: a more game-like structure with several possible actions, sound, and a spotlight effect I've never seen in Twine before. All these factors do an excellent job building atmosphere and creating claustrophobia. The music at the end is perfect.
I give my father's long, long legs four stars on account of the story, mood, and some excellent use of Twine's possibilities. However, players who prefer some agency in their IF might want to look elsewhere.