installing the HP Prime on Android

[TheKaneB]

Yep, the Google Drive app basically only works by itself. It's poorly integrated with third party apps.
As Tim said, in Android there is a mechanism called "Intent" by which one app states the "Intent to open a certain type of content" and the OS does the rest. If the PDF reader advertises itself as being capable of opening that content type (through specific Intent filters in the application manifest), then it will work.