Any software used to read a document, open a picture, play a song, or play a video can capture the information regarding the file, store it within the app and send it somewhere if they choose to do so. They only way you can ABSOLUTELY be sure they are not doing so is to have someone hack the app and make sure it contains no such code.
What are you so worried about? If you are watching pirated commercial movies (please don't steal media) it is doubtful anyone, including the developers of Player would care. They might care to collect what you watch if they can sell your preferences to another company that could then attempt to sell you similar titles. If you are watching adult movies the developers aren't going to care, with the exception they might sell your preferences to a company that sells adult titles. If you are viewing child **** or snuff films they probably will care and will contact the authorities and you will be arrested.
Since dilbert41 has this software perhaps he can check his documentation and see if they have a privacy policy. Or you can write to the developer and ask to see one. Or you can turn off WiFi, BT, Cellular, etc. and make sure this iPad NEVER connects to the internet.