The rules for wins and draws in Shogi are not really more complicated than those for Chess. Main difference is that in Shogi perpetual checking is forbidden (i.e. the checker will lose at the 4th repetition). It is Xiangqi that has the complex rules for deciding repetitions (perpetual chasing).
The low draw rate is not a consequence of these rules, but of the fact that captured pieces are recycled. This means the game doesn't peter out for lack of material, as in Chess, but that the possibility for a decisive attack remains present forever. Crazyhouse also has a very low draw rate. (Although perpetual checking is allowed there.)
BTW, that this would be the "clearest illustration of moves" is debatable. Personally I like interactive diagrams (where the moves are shown when you click on a piece) better. Such as at http://hgm.nubati.net/rules/Shogi.html . Especially if there are very many piece types, such as in Chu Shogi ( http://www.chessvariants.com/report/chu-shogi ).
The clearest illustration of the moves of different Shogi pieces can be found from the following pdf file.
http://veryspecial.us/free-downloads/AncientChess.com-Shogi.pdf
What you can’t find are the quite complicated rules regarding wins and draws. According to one source, draws in Shogi are rather rare, as rare as one percent !