The way I'm reading it, nodes pay their neighbors for successfully delivered packets using bitcoin-like credits mined by specialized nodes. I'd imagine the nodes with high balances would then be prioritized for delivery (both sending/receiving).
If that's really how it works then my gut instinct tells me it's wrong. We shouldn't rely on any form of currency exchange for negotiating the movement of web traffic, otherwise we risk messing with net neutrality. Bandwidth should be balanced by tracking load, not by currency.
Cryptocurrencies could prove useful as a form of identity on the network, a secure ID token that isn't traded but does allow nodes to recognise each other, I see the merit in that.
But can these people built a better Tor network/tunnel than the Tor/EFF people did? Doubtful. Libernet seems based on Linux, itself not secure. My group has solved both this problem, without using security flawed Linux/Unix (I will be happy to send you the scientific papers proving my point. See my HN profile).