The Father hears in secret

The verse before this one is the key to it. Some people pray where they can be seen, and Jesus says they have already received their reward in full - they wanted to be watched, and they were. That is the whole transaction, completed.
So the shut door is not a rule against praying with other people. Jesus prayed alone, with his disciples, and in front of crowds. It is a test of motive. And the reason it works is given two verses later: your Father already knows what you need before you ask him. There is no audience left to perform for, because the only one listening was never going to be impressed anyway.
Scripture links:
- Matthew 6:5-6 - "they love to stand and pray... that they may be seen by others... But when you pray, go into your room and shut the door and pray to your Father who is in secret."
- Matthew 6:8 - "your Father knows what you need before you ask him."
Nobody has to hear it for it to have been heard.