I have been studying Japanese for almost a year and I think you need more than just Elementary Japanese. I say to have a basic understanding, one should at least finish Intermediate or even Advanced Level Japanese.
Also, you can't really understand what they saying just by looking up the words as the sentence structure is completely different from English. This is because Japanese uses a Subject-Object-Verb sentence structure. For example...
アリスさんはりんごを食べた。
(Alice ate an apple.)
Also, the text is automatic, so you have to pause the Game. Still, to better enjoy the game, one should at least have some formal lessons or self-study from lessons.
As for the dictionary, I use Kotoba (which is under a different name now). But, if you are interested in learning the language, Genki I and II is good text books to learn from... Just be aware that a mix of short forms and polite forums are used in the game.