"Sufficient personal network to apply to work at Built For Me via a personal recommendation rather than just submitting an application through AngelList."
This is vile.
This is vile.
They're just explicitly stating that although knowing the right people is not a requirement, it will work a lot better in getting you in the door.
My current company, in fact, has grown almost entirely from employee recommendations, and it has worked out well. The fact that you know someone is good from previous experience greatly reduces the chance of getting someone who doesn't work out.