I agree with Zeldaskitten. The newer games in the Dragon Quest series are rated Everyone 10+, so it makes sense that many kanji would be left out. I’ve noticed in anime, if the viewing audience is generally younger, the lyrics to the theme song are on the screen, but with furigana on all the kanji. Since your game was on the original NES, they probably couldn’t script furigana into the text-blocks, or lacked the necessary space.

It’s good to practice things that are meant for children when you’re still learning; so, good for you. I’m looking for Japanese-language Disney movies, myself.