Latency is just another bit of randomness. There have already been examples of using latency across the internet to extract encryption keys because e.g. someone didn't compare the checksum to the entire string and simply stopped once it was clear it wasn't valid. That's detecting nanosecond differences across a hundred-millisecond extremely noisy channel.

Besides, if you can get the output, you can tell how many rolls occurred, so it doesn't really matter. And this is a "chosen cyphertext" example, so the attacker has some idea of how long the computation will take under certain circumstances.