It appears to be a type of currency where new units are created by credit, and extinguished by repayment of credit. This makes it somewhat similar to mutual credit systems or to the models presented by Black, Fama and Hall (except the latter ones use interest).
In my opinion, systems like this require an exogenous definition of the unit (irrespective if it is, in reality, convertible). Therefore, it is strictly speaking not money in the narrower sense (like Bitcoin), it is a money substitute. If this link to the definition of unit does not exist or is severed, unless there is some other mechanism for braking the production other than the expansion of credit itself, the supply would increase until the cost of production and the market price equilibrate, which from a practical point of view means hyperinflation. Since BIBO appears to have a decentralised decision mechanism:
A Member is free to deny performing a Transaction with another Member.
there appears to be no braking mechanism and it would be produced until the market price falls down to production costs.
It is also unclear to me how rules are enforced. As they refer to empirical data external to the BIBO network, rule breaches might not even be detectable. Also, what happens if someone goes bankrupt (noone wants to lend him anymore)? How to prevent people from accruing more debt onto new accounts? How to prevent someone from granting credit to himself (between two accounts)? These however are technical problems, not economic ones.
The claim that it is stable because inputs equal outputs is misleading. Both Mises and Rothbard already pointed out that expansion of credit is only limited by the requirement to redeem the money substitutes against money base and/or a monopoly position (or at least regulation as we have in banks) of the issuer. Absent this, the only other limit are the production costs. Merely because the system can have a defined equilibrium does not mean hyperinflation can be prevented. Any issue of money while its purchasing power is higher than the production costs redistributes purchasing power to the producer, therefore the optimal strategy is to produce as much as you can.
Last but not least, I do not see an answer regarding how to motivate people to use BIBO instead of any other currency. I argue that the choice of money is driven primarily by transaction costs, not necessarily by the features of the money supply. Unless BIBO offers lower transaction costs than Bitcoin, it cannot compete with it. So it would have to be forced on people anyway.