You would still need to create the models to print (say, with a program like blender) or download them from somewhere, but yeah, 3d printing would be ideal for this sort of thing, and far easier to use on the long run. As for the rules, they seem quite appropriate to the theme. 
I don't have any experience with 3-d modeling software, so I should probably work on learning that.
Out of curiousity, are there 3-d scanners available as well? Or are those pretty pricy? Either way, I can't afford it, but would be a nice toy for down the road. 
I'm under the impression that there are some affordable 3d scanners out there, but I haven't really looked into it yet to be honest. On the other hand, you have plenty of models you can download from the net, in sites like thingiverse, for example:
Mario and Bowser - http://www.thingiverse.com/thing:338542
Mario figurine stand - http://www.thingiverse.com/thing:231246
Yoshi - http://www.thingiverse.com/thing:211601
Mario - http://www.thingiverse.com/thing:27678
I haven't checked all the models, but they seem to be fairly high quality, and should be printer ready. Have fun.