^That's right. Trelane not only admires Napoleon, he's aware of the death of Alexander Hamilton, which took place in 1804. Also, the Johann Strauss waltz he makes Uhura play on the harpsichord was composed in 1880.
The episode makes it clear that Trelane doesn't realize the significance of the speed-of-light lag in his observations:
JAEGER: Notice the period, Captain. Nine hundred light years from Earth. It's what might be seen through a viewing scope if it were powerful enough.
TRELANE: Ah, yes. I've been looking in on the doings on your lively little Earth.
KIRK: Then you've been looking in on the doings nine hundred years past.
TRELANE: Oh, really? Have I made an error in time? How fallible of me. Oh, I did so want to make you feel at home.
Thus, the episode explicitly establishes that the events of the 1800s -- as late as 1880 -- are 900 years before the episode, putting it in at least 2780. Although anachronistic music selections in fiction are not unheard of, and we could rationalize that maybe Trelane took the waltz from Uhura's memories, but that would still put the episode after the year 2704.