Whilst it is certainly possible to export (print) Visio drawings and diagrams (.vsdx) as .pdf documents, it does not make much sense to try to convert vstx to pdf, i.e. export Visio template as PDF document, considering templates are usually just "empty" documents that contain settings for making new files.
But in case the template actually offers some graphics content, it may very well be possible to export vstx to pdf in Vision, hence essentially perform vstx to pdf conversion - whatever the actual purpose may be. Unfortunately, no other program can work with .vstx templates, so Visio is the only choice.