I've seen a few spectacular Tiffany Coin Silver Tea Sets, and they have that "dot" instead of the designation "ENGLISH STERLING" which is quite similar to your example. I see your point about being unsure about how to catalogue this Tea Set, as Coin Silver or Sterling Silver. We can still talk about rarity, and obviously the coin silver tea sets are more uncommon than the sterling silver tea sets, as they were only available in the early days of Tiffany.
Did whoever stamped the hallmarks just run out of room, so the "ENGLISH STERLING" hallmark was omitted? That is a possibility.
Even if you had it acid-tested (the most commonly-used assay method of Gold & Silver shops and pawn shops) by an expert with decades of experience testing silver, you would still just have an opinion that the silver tested strongly for sterling silver. Did you have it acid-tested, and in the opinion of the person who performed the test, was the result consistent with "Sterling Silver" and not "Coin Silver?"
To really know for sure, you could find someone who has an "XRF Testing Device" which is a hand-held scanner which tells you the exact level of Silver, and a coin silver composition from the 1850s would look something like this:
I'm voting for Coin Silver, just based on the other Tiffany Coin Silver Tea Sets I have seen.