Miners are not needed for NEO.
NEO is using the Delegated Byzantine Fault Tolerance consensus protocol. NEO holders verify transactions and earn a GAS stake for doing so, proportional to the amount of NEO hold.
You can collect the GAS by executing a smart contract.
You also have many projects built on NEO that chose to airdrop tokens to NEO holders instead of doing ICO. Ontology did so a few weeks ago.
NNS Neo Name Service will too.