and another deer notices this. As Alnilam and I both said, it doesn't have to be visual - it could be by scent, which sticks around for a while.
One frightened animal can easily spook a whole herd - that's how stampedes happen.
And the does have got to be around the stags sometimes, or else where do baby deer come from???
hunting season is a different time of year to mating season, but that doesn't mean the does won't observe the stag being frightened of a passing human at that time, even if the human isn't actually hunting).