As you said, more computation is required if the block size is bigger. But mining nodes (initially) do the actual computations - they include transactions in a block and execute the transactions. So if there are more (or more complex) transactions more computation is required from the mining nodes. Other non-mining nodes do various levels of validations (and possibly also execution) on the blocks.
So the sentence makes sense. Although adding some more transactions in a block doesn't make the actual mining process much slower - calculating the mining puzzle takes most of the time anyway and for that it doesn't matter how many transactions there are as long as they have been executed.
The mining process goes something like this:
1) Miner sees unexecuted transactions and decided which ones and in which order to include in his block (probably based on monetary incentives: biggest gas prices)
2) Miner executes the transactions in that order
3) Miner gets the end state and therefore the block hash and uses that to try to solve the mining puzzle