Mini Media Player may save some some user data locally on the device it's running on. This data includes any settings/preferences you change, it also includes videos you watch. Mini Media Player saves videos you watch so that you can reopen them quickly later. All of this data is stored locally on the device which Mini Media Player is installed and not shared anywhere else by the app.
As Mini Media Player connects to websites when you play online videos, those websites may collect data (Similar to if you played them in a web browser). If you would like to know what data may be collected, ensure to check the privacy policy of whatever website the video came from when playing an online video.