It has been investigated by game translators, and the most likely reason is that Japan, like most country in the world, have English classes. So Japanese, even in the 80's, knew to read some English words.
English words were used simply because of space.
English words can be written using 26 characters. If you only use menus options, chances are you can use only one simple font and all in uppercase, so you really need only 26 characters.
On the other hand, while Japanese English classes teach them lors of word lists and grammar rules, they are very poor at teaching them how to actually construct and understand english sentences. (a point that is very proven by the broken translations of so many games on the NES era) So a game written in english would be unreadable to them.
On the other hand, Japanese kanjis and hiraganas (to my understanding, they are two different writing systems) convey so much nuances that what would be a generic phrasing in English, with the change of only two kanjis in a sentance, tells you about the sex, rank, role of the character talking... and this, even if you don't actually SEE the character on screen; Japanese dialog are much richer and convey more information than English. It's one reason why so many Japanese games included text - What for us feels like sone generic sentences between the good and the bad actually carry much more for them.
So in short, English is used to save space, but Japanese is used to better convey the story.
