Does glutinous rice contain gluten?
No, it doesn't. Rice is always gluten free. 

It just so happens that words like "gluten", "glutinous" and "glue" are words which have a common root, meaning "sticky". Glutinous rice is sticky due to a high proportion of bushy starches in the rice grain. It has nothing to do with gluten, which is a complex formed by wheat proteins, and not contained in any type of rice. 

See also our list of gluten-free grains, which also notes the gluten-glutinous distinction.