It's not only about whether the parties know each other, it's about how they can verify that they're all behaving according to the rules of their contract.
In multi-party scenarios, you often find intermediaries whose primary function is to act as a centralized, trusted exchange for the other parties, performing the job of the banker in the sentence you quoted. One reason this is needed is that without them, there's a lot of room for collusion between parties that deal with each other directly.
These intermediaries do currently use "more generic software", but you still need a company to run and operate that software. Blockchains can replace such companies, or at least replace one of their main reasons for existing.
In many cases, it would be possible to come up with an application-specific approach to securely and verifiably operating multi-party transactions without intermediaries, but that's not done much because it's generally just easier to use the intermediary model. Also, implementing secure decentralized transaction systems is outside of the the core competencies of the companies that need such capabilities.
Blockchains provide a generic, non-application-specific approach to implementing a secure, shared, distributed ledger, so that applications can focus on generating the transactions and not worry about the issues involved with securing a shared ledger.
In multi-party scenarios, you often find intermediaries whose primary function is to act as a centralized, trusted exchange for the other parties, performing the job of the banker in the sentence you quoted. One reason this is needed is that without them, there's a lot of room for collusion between parties that deal with each other directly.
These intermediaries do currently use "more generic software", but you still need a company to run and operate that software. Blockchains can replace such companies, or at least replace one of their main reasons for existing.
In many cases, it would be possible to come up with an application-specific approach to securely and verifiably operating multi-party transactions without intermediaries, but that's not done much because it's generally just easier to use the intermediary model. Also, implementing secure decentralized transaction systems is outside of the the core competencies of the companies that need such capabilities.
Blockchains provide a generic, non-application-specific approach to implementing a secure, shared, distributed ledger, so that applications can focus on generating the transactions and not worry about the issues involved with securing a shared ledger.