They might have phrased this poorly.
>We should support at least 100,000 simultaneous users.
This line makes me think that this is what they expected the peak (or near peak) to be.
>Users can place one tile every 5 minutes, so we must support an average update rate of 100,000 tiles per 5 minutes (333 updates/s).
So assuming that they mean that 100k is the peak and that clients are limited to 1 update per 5 minutes, they can expect 333 updates per second on average. The "average" is taken over this 5 minute period. This average represents the number of queries per second they will get if everyone's 5 minute cooldown is spread out evenly over each 5 minute period.
It is possible, for example, for half of the peak population's cooldown to expire at 1300 and the other half to expire at 1305. In this case the average updates/s over the 5 minute period from 1300-1305 would still be 333 updates/s even though there were really 2 bursts of 50k a second at 1300 and 1305. It's far more likely that cooldowns are not excessively stacked in this way, so you prepare for the average and hope for the best.