I don't know, I read their T&C and they are mention the following "10. Prize and Related Terms. One Winner may receive a prize of one (1) Bitcoin or, " < I don't like that "may".
They will surely ask you to demonstrate your method and it has to be reproducible and independently verifiable. They also talk about how they don't want compilation tricks that can't scale.
Your method should be as general and robust as possible. It should not require impractical amounts of classical compute to scale to 256-bit keys. (For example, we're not interested in approaches that use compilation tricks that don't scale.)
https://www.qdayprize.org/How many people have access to quantum computers? I would expect the budget involved for the ones who have to far exceed 1 BTC, which makes me think this small prize isn't worth their effort.
Good question. I guess not that many. But those with enough money to spend can surely find access. IBM, Google, and AWS provide cloud quantum computing services to anyone willing to pay.
What a paradox!
They are asking participants to break the Bitcoin cryptography then they want to pay them in bitcoin which would become worthless if they succeed

True. But they don't really expect anyone to succeed. They have said that if anyone can break a 5-bit key it would be an astonishing achievement. And that's wide of the 256-bit mark.