I cried, and the game filled me with dread at the thought of growing old. This game is definitely succeeds in inducing intense emotions, which I assume was the intent, so great job.
As for the card "gimmick": to really tell whether it was effective or not, I'd have to visit an alternate reality in which I played the game without it, but I like to think that it made me more engaged in the story, especially early on. It certainly did not detract from my experience, and it was integrated in the story in a clever and emotionally impactful way.
Also, the scope of the game feels just right, and as an outsider to the development process, I can't think of anything to add or remove that'd improve the game. Not only that, but what's in the game is polished to the point where I could easily recommend it to people without the context of it being a jam game.
All in all, great game!