In some ways, Raiders of the Lost Ark on 2600 is closer in design to Zelda than Cloudy Mountain, i.e. with the way inventory works like using explosives to open passages. It's possible Miyamoto played early action-adventures but it's also possible that the similarities are coincidental.
That's the problem with talking about influential games: unless the developer tells us their inspirations (like Westwood giving credit to Herzog Zwei for RTS influence), it's just guess work. Inspirations could be be obscure or popular. Japanese developers seems especially unlikely to credit other companies' works.

