I had no idea, but according to Wikipedia, the first video game to offer a high-score table, in which players could record their score and initials, was Star Fire. It was also released in 1978 and was the first sit-down cabinet machine, too. I always thought "Star Wars" was, but I guess not.
My entry for Starfire for the C64 can be found on my blog here: https://www.my64.in.nf/doku.php?id=library:starfire
My entry for Starfire for the C64 can be found on my blog here: https://www.my64.in.nf/doku.php?id=library:starfire