He won the Nobel Memorial Prize in Economic Sciences, which (as far as I can tell) was established later than the other prizes but is managed together with them with the same foundation and ceremony and so on.

Is the distinction between it and other Nobel prizes useful here?

It is relevant since the Nobel prize in economics indicates academic achievements in the field of economics.

If it would've been a Nobel prize winner for peace there would be little signal attached to it regarding the economic quality of the block chain project.

Yes. It is funded by the Swedish Central Bank.

Would you trust a Nobel prize in computing funded by Google?

Yes. The closest thing to the Nobel Prize in computing is the Turing Award, which is indeed funded by Google.

Although it is not Google who decides on who wins, and the Award would still be reputationally valuable if there were no money attached to it.

Funding rarely determines process or outcome.

It's a common argument, but unworldly, given that there are huge amounts of largely autonomous institutions that rely on single donors, may it be public or private money.

"Would you trust a Nobel prize in computing funded by Google?"

Would you trust a Nobel Peace Prize funded by an arms merchant?

The Turing Award? Yes. It is considered by Computer Scientists to be the premier award in the field.