To claim your copy (which, by the way, is a spectacularly good game), just log into your GOG account—the same one you used for the Gwent closed beta—by 8 am ET on May 29. Click the buttons as necessary, and blam, free game for you.
To mark the forthcoming launch of the Gwent public beta, GOG is also having a "Role-Playing Week" sale, with discounts of up to 85 percent on games including The Witcher 3: Wild Hunt and its DLCs, Pillars of Eternity, Tyranny, System Shock Enhanced, Legend of Grimrock 1 and 2, Vampire: The Masquerade – Bloodlines, Deus Ex 1 and 2, and more.
The Gwent public beta is scheduled to begin on May 24, and the GOG sale will be on until May 29. CD Projekt Red ran a Gwent "Public Beta Preview" livestream last week on Twitch that can you catch up with below.