>It is not trying to say that this currency is not countable or something like that (how would that even work?)

Yeah, that's what I thought at first, as well as some other people. I thought that maybe each person creates their own "currency" - maybe all the transactions are just sending files? The people trading determine the currency - a rare (e)book? Photographs?

I feel like it'd be very useful to make this clearer. "No amounts" is a very different statement than "no public amounts".