The recent proliferation in mobile touch-based devices paves the way for increasingly efficient, easy to use natural user interfaces (NUI). Unfortunately, touch-based NUIs might prove difficult, or even impossible to operate, in certain conditions e.g. when suffering from motor dysfunction such as Parkinson's Disease (PD). Yet, the prevalence of such devices makes them particularly suitable for acquiring motor function data, and enabling the early detection of PD symptoms and other conditions. In this work we acquired a unique database of more than 12,500 annotated NUI multi-touch gestures, collected from PD patients and healthy volunteers, that were analyzed by applying advanced shape analysis and statistical inference schemes. The proposed analysis leads to a novel detection scheme for early stages of PD. Moreover, our computational analysis revealed that young subjects may be using a 'slang' form of gesture-making to reduce effort and attention cost while maintaining meaning, whereas older subjects put an emphasis on content and precise performance.