What does the treasure chest icon on a Shrine's tooltip (next to the Shrine's name) mean? Does it indicate that there is an unopened chest remaining, or that you have found all the chests?
From what I can find, the little treasure chest icon means you found all the chests in that Shrine.
Yes it means you got them all in the shrine. Good for completionist runs
means you got all the chests in that shrine. If your other shrines don't have it, it means you missed some of the bonus chests
The icon appears if there are no more chests to open in the Shrine, and appears even if there's no chest at all. If there wouldn't be any blue chest icon next to a Shrine with zero chests, people would spend hours and hours to look for a chest that doesn't exist and get very frustrated.
One more GameFAQs that says the same thing (didn't bother to include a quote).