There's a "rule" in bitcoin code that tells to give the miners the right block rewards. But the coins go to miners' wallet also as transactions. The block reward is just a special transaction and the miner, if he doesn't spend it, will have an UTXO in his wallet.
Note that the coinbase rewards and the fees must both be claimed by the miner (this will become the first transaction of the block). If it does not claim the coins, they are lost forever, and not even private key recovery will reclaim them because they do not have an associated address.