Ethereum – What’s the Block Reward for Smart Contract Miners?

When talking about a cryptocurrency, the block rewards are new coins given to the miner, right?

yes

I guessed that the reward for miners of smart contracts are the native tokens

Also you are correct. Smart contracts are deployed via transactions. Hence mining a smart contract is also just another transaction and miners are rewarded using native currency, Ether.

As per the link provided, the confusing part of the article is

Miners essentially ensure, or “validate”, the transactions within each block to guarantee the blockchain’s integrity and are subsequently compensated through block rewards as well as transaction fees. They are the engines of the blockchain, with block rewards and fees being the “gas” (not to be confused with Ethereum’s “gas” which powers smart-contracts) that compensates and fuels their work

As I feel, here the author tries to highlight the fact that block rewards and fees are the reason why miners mine. As block rewards and fees are needed as incentive for miners to mine, author tries to metaphorize(to show a similarity) it with gas to an engine.

Since he is generally speaking about blockchain, he specifically mentions that it is not the term 'gas' in ethereum he is referring to. While aforementioned fact (the idea of miners need an incentive) is valid in ethereum ecosystem as well, in ethereum the term 'gas' is a keyword and is referred to the unit that measure the computational work a miner has to do. E.g. for an addition operation a miner has to spend 3 gas.