The application is distributed as a zip file, so you should extract the exe from within the zip file and deploy that.
To silently install the application, run its setup file with the arguments /exenoui /qn
/exenoui supresses the self-extractor dialog
/qn makes the packaged msi silent, but you could use any other msi arguments here
Setup Type: Windows Installer (Delivered as an EXE)
Deployment Method Used: Vendor Provided Command Line (switch driven)