What you show us is pairwise plots and you have multivariate data. It does not have to be the case that any of the variables individually let you to do accurate predictions, but nevertheless it does not mean that the combinations of variables would not let you to do so.
Check this example, where the corelation changes from positive to groupwise negative when introducing another variable.
In fact, if you look at the paper by Erdogdu et al (2013) that is provided as a reference for this dataset, you'll learn that the authors actually were able to make predictions that were better then random guessing using this data.
Erdogdu Sakar, B., Isenkul, M., Sakar, C.O., Sertbas, A., Gurgen, F., Delil, S., Apaydin, H., Kursun, O. (2013). Collection and Analysis of a Parkinson Speech Dataset with Multiple Types of Sound Recordings.' IEEE Journal of Biomedical and Health Informatics, 17(4), 828-834.