The headline doesn’t match the story; Trajan conquered Dacia, so the palace would have dated from his time; his successor (Hadrian) wasn’t keen on holding on to Dacia, but there was a Roman presence there for a long while. Trajan for his part didn’t stick around Dacia; he was one of the most effective conquerors the Roman Empire ever produced, maybe the most, and he had other asses to kick. He did build Trajan’s Column in Rome to commemorate the conquest of Dacia, and his reign (in particular, that very conquest) marks the economic highwater mark for Rome.
So, instead of being an official palace of Trajan’s, this was more some Roman villa where “Trajan slept here”?