Random Thought: "The lion and the unicorn were fighting for the crown... (Now I hope that's stuck in your head too)."
This game felt like a training exercise, perhaps another first attempt? I feel like I have gotten several of those in a row. If so, welcome all newbies to this wonderful world of anything goes!
But that said, players still expect a certain amount of internal logic, even when you are dealing with magic any mystery. It's important to keep track of motivations, rules, etc. These are the things that make magical stories relatable, otherwise player are asked to figure things out several times over. When you ask players suspend your disbelief, you need to stick to one clothesline, otherwise players get their panties in a bunch. (You see? That horrible metaphor was understandable because it was internally consistent.)
The other thing that players like in games is some challenge, or at least the feeling that they know what to do next. Part of this has to do with that internal consistency I mentioned. When you have a magical system and know how it works, you can anticipate what you need to do next. I suspect many of the, "talk to unicorn" obvious prompts could have been cleared up with some more dedication to creating that narrative and consistency.
But do keep writing, I think there is some good potential here.