It’s not the age of the print, it’s just the print itself.
You’re comparing two very different film stocks/processes. And two films that were shot very differently (Leia on the Tantive is very bright, Leia in the Hoth base is dark).
To answer your answer: yes this film was more than likely that grainy in 1980.
I don’t know when people last saw an actual film print in a theater but whenever my local art theater has a film print of an older movie I am surprised by how soft it looks. Even a modern film like The Game which I saw a couple months ago was soft and grainy.
Technicolor prints (and nitrate prints) are amazing to watch projected. Cheap Eastman prints… meh.