much simpler than this. A saw (any kind or type) and lots of sandpaper (lots and lots) of rough to fine grits. Finish.... optional but lots of wax or oil seems right. Christmas is coming and this project is a good one to involve smaller hands for the work and for the idea of making gifts and stuff rather than just buying. Signing and dating the set or the baseboard might be a nice touch for the kids.
http://smartgirlsdiy.com/2013/12/3rd-da ... ant-jenga/http://www.jenga.com/about.phpNote: On this page find a download for a JENGA winners cerificate you could copy and add to a set.
Food color would make a nice safe colorant to add some variation to your blocks, just WEAR rubber gloves.