What are Cassava sticks (Tapioca sticks) used for in Thai cuisine, if at all?
Those seem to be Cassava stem cuttings. They're not meant to be eaten, but are instead meant to propagate new plants.
Cassava are able to grow in poor quality soil and can survive harsh dry seasons. They also do well in areas that do not have good irrigation. This makes them popular in Thailand, especially in poorer areas.

Note that Cassava is not considered a staple food in Thailand. You will see a few uses for it in Thai Cuisine, such as Sweetened Cassava, but more importantly Thais consider it a good cash crop to export.
Cassava require minimal care and cost and can be used for many purposes, such as:


Chips/Pellets to be used for animal feed
Flour for confectionery
Starch for infant food
Starch to be used in textile industries
Ethanol