1. Unpredictability is possible even when the user doesn't have any choice about input (type keys based on a PRNG)
2. Predictability is possible even when the user can choose from both available options (human user)
It's an interesting study in our ability to be random, but it doesn't tell us anything about the macro-level philosophical concepts of determinism or free will. Compatibilism is not relevant to this demo.
From a physical point of view, free will doesn't make sense. Laws are deterministic at macro level and contain some randomness at the lower level. Neither are free will.
Also, there is a huge assumption there - the assumption that there is a "self" that can have this free will. There is no self, just a stream of experiences and actions. The "self" is an intuitive concept, a reification that is useful in social dealings. Taking it from the social context and putting it in the realm of physics could be just a sleight of language - it cannot be the same concept in both domains, because the two domains are so far off. And trying to formally define a self in physics is impossible for us.
I mean, ever heard of compatibilism?
https://en.wikipedia.org/wiki/Compatibilism