I live in Bali and love the kites here.
Most of the medium sized kites are made of plastic (like yours) but instead of taping the plastic they use mosquito coils to melt the plastic together.
The spars are split bamboo and the designs are often animals (instead of geometrical shapes) like owls and fish.
I have tried building them myself but I'm not nearly as good. I can't get the plastic to be tight, but some have flown. I also use tissue paper because it looks good. Recently I modified a Bali tourist kite (one of the foldable ones which look like birds, dragons etc.) to a steerable stunt kite by just simply attaching two bridles on it.