I'm already a part of the patreon and own the alpha, but why does it say $20 on the game page?

The Patreon integration is a relatively recent addition to the Itch interface, so Itch still requires assigning the game a price even if it's not meant to be bought.  The $20 price is just a placeholder; it may ultimately be more or less when the game is completed, most likely hinging on what Steam recommends for a price point!