Publica https://publica.com/ claims to be a protocol that is built on the Ethereum blockchain, what does this mean on a technical level? Will Gas be utilized to execute smart contracts on Publica protocol?
Yes gas will be used to execute smart contracts as the protocol is built on the Ethereum blockchain. Think of Protocols as middleware to ease various processes. It will most likely ease some process by removing the trust layer and append to protocol rules.
Looking more into the reference, I can confirm that the publica protocol is simply a definition for a smart contract which consist of rules (price etc.) allowing publishers to fund book publications and ultimately reward funders (token holders) with a copy after completion.