He seems to be saying that if the block is too big, he might need more time to validate it than the time the network takes to solve a new block. This would mean he loses time with every block, and therefore can't validate at all.
Bitcoin blocks are solved every 10 minutes on average. He suggests that if blocks take him 11 minutes on average to validate he would lose a minute every block, therefore he would be unable to validate every block, which defeats the purpose.
With the assumption block sizes will increase, I'm unconvinced this problem is even on the horizon. In answer to the question "how long does it take", this excellent answer refers only to seconds, not minutes. For validation to snowball into an 11 minutes long process, we'd have to willfully neglect it's long predicted coming. I doubt that would ever happen.
But that's an extreme example. In reality, going from 5 seconds to 15 seconds really seems insignificant at first, but it does have advantages for larger miners over smaller miners.
A significant portion of blocks are found within seconds of the previous block. If you found the previous block you can skip validation and begin working on the next block immediately. This means you will get lucky every now and then and shove the next block within a few seconds, allowing you to claim the reward and fees. Comparatively, if a different miner solves the next block within a few seconds, he will submit it without any transactions because he was still validating the previous one. Naturally, large miners find more blocks, so they are more likely to benefit from this.