A treat is generally something that tantalizes the senses or is something refreshing from the ordinary in life.
Some can consider going to an uplifting movie a treat. It takes one out of the ordinary day of life for a while.
Ice cream is considered a treat because it tantalizes the senses through taste buds and tends to take us away from the ordinary of life even though just briefly.
I think a treat is most anything that causes us to experience an enjoyable sensation.
It could even have been a ride in the back of uncle Joe's pick up truck around the farm and down to the lake and back. That would have caused one to experience an enjoyable sensation after a day or week of toiling on the farm.
When Starbucks uses that word it would most likely trigger what I have described above and the idea that comes to mind is the, if just partially, escaping of the ordinary moments of life through some tantalizing of the senses.
Its a very effective trick.
We are very easily tricked by something which causes us to experience an enjoyable sensation, even if just for a brief moment.