Cool idea! I like that you decided to go meta with the setting.
One thing I wish would be different is a randomisation of the level, whenever you spin the dice. This kinda goes against the main idea, but maybe it would be better to just give levels in order (you can even still pretend the levels are selected randomly). Player would naturally want to see all the content of the game, instead of getting the same level multiple times, and you can start giving out random levels if the player decides to keep playing.
Also controls are a bit evil in this one, I felt like at some points I was denied my right to double jump due to being to close to a wall. But overall - great platformer with lots of replayability, good job!