A Nakamoto Type I civilization would be one that converts all available power of a planet into waste heat and funny numbers, a Nakamoto Type II civilization does that with all the power output of a star and so on... basically the Kardashev scale [0] but with the restriction that useful output SHOULD NOT be produced [1].
Edit: lowered requirement level from MUST NOT to SHOULD NOT to allow for situations in which a limited amount of energy could be expended to either increase the hashrate further or to get closer to the limits of computation [2].
Edit 2: the more I think about it, the more it reminds me of the Universal Paperclips game.
[0] https://en.wikipedia.org/wiki/Kardashev_scale