You're missing what "performing transactions" actually means. The blocks are the transactions. Nothing is valid if it's not included in a block that is part of the canonical blockchain. Miners are the ones who assemble blocks from several transactions, and link them to the blockchain.
Things like side-channels are performed off-chain, but are still settled and only valid on-chain. Since they are side-chain, there is no gas or transaction fees (unless that's part of the specific transaction), and mining isn't required until settlement, which is on-chain.