What property does rice flour add to a shortbread recipe?
There are numerous recipes also calling for corn flour or corn starch instead of rice flour; so you can substitute with any gluten-free and low-protein flour or starches (also potato starch). The idea, is pretty simple actually, cutting down the protein content of the mixture.

Considering there's a good amount of fat in the shortbread, it will inhibit the development of gluten.

Adding riceflour will help you utilize these two measures, in our battle against gluten development, resulting in moister and less chewy end results.

And please note that, afaik, the traditional recipe actually calls for oat flour. (which, i believe, is also gluten-free)