Breakdown of O eski kıraathaneye gitmeyeli müdavimler tamamen değişti.
o
that / he / she / it
gitmek
to go
eski
old
değişmek
to change (intransitive, undergo change)
Questions & Answers about O eski kıraathaneye gitmeyeli müdavimler tamamen değişti.
How does the negative verb gitmeyeli end up translating to "since I last went"?
The suffix -(y)alı indicates the starting point of an elapsed period of time. When you attach it to a negative verb like gitme (not to go), it literally means "since the state of not going began." In English, it is much more natural to translate this span of non-action as "since I last went."
There is no personal ending on gitmeyeli. How do we know it means "since I last went" rather than someone else?
Converbs like -(y)alı do not take personal suffixes. The subject of that clause has to be understood from context. If a speaker states this out of the blue, they are usually talking about their own experience. If they wanted to specify someone else, they would add an explicit subject pronoun, such as O eski kıraathaneye Ahmet gitmeyeli... (Since Ahmet last went...).
I see kıraathane is translated as "coffeehouse." Is this the same as a kafe?
Not quite! A kafe is a modern cafe where you might buy an espresso. A kıraathane (historically a "reading house") is a traditional Turkish establishment, mostly frequented by older men, where people drink black tea and play games like backgammon or Okey. The patrons of such places are exactly who you would refer to with the word müdavimler (regulars).
Why does the sentence use the simple past değişti (changed) instead of a tense reflecting an ongoing state?