To export a recording (GPX file) you simply need to go to GPX Recorder > Recordings > select the recording from the list and press Share.
When you share the file, Android will show you all the installed apps to where you can share it, usually you would select something like Google Drive to store it online, but you can also select your email app if you want to send it by email to someone or even select an instant messaging app if you are sharing it in a chat.
https://youtu.be/1yKqlMK0YPA