The Japanese board-game 人生ゲーム has given rise to many, many adaptations. Some of them can be used for level 1 language-practice (some with more Kanji than others, etc.). All of them make use of exactly the sort of vocabulary that beginners need to learn (and practice), i.e., basic terms related to work, study, life, etc. etc.
Click below to see marriage, Japanese style, according to "The Game of Life".
Apparently, in Japan, you just point your finger at a random house, and then propose marriage to whoever is inside; or, at least, this is how the process is idealized and taught to children in "The Game of Life".
I don't know how much time I'll have to work on this, as the term now resumes, and I have to engage in rote memorization of lists of Genki vocabulary, but, overall, I wish I had thought of this method sooner. A quick google search reveals that there are many, many websites discussing the possibility of learning Japanese through video-games (most of them presuming intermediate-or-better language ability). However, very few games really revolve around basic, useful vocabulary in this way (i.e., it isn't science-fiction, and it doesn't involve castles or swords, etc., and even the grammar tends to be in simple statements of fact).