Update: Valve has officially announced the draw. Here's how it will work: "Each Steam-initiated, non-limited account will receive a draw entry while watching the broadcast [on Steam]." Steam will randomly select 150 lucky winners of eligible participants every 15 minutes, and each winner will receive a game that they do not possess. the remaining prizes. " The draws will be executed for the complete transmission. The original story follows below.
If you're watching The Game Awards tonight, you might want to watch on Steam, or at least have the broadcast open on Steam. If you do, you'll apparently have the chance to win a free copy of a nominated game, so some of the best games of the year are included, including Divinity: Original Sin 2 and XCOM 2 plus War of the Chosen DLC. You can see the complete list of prizes here.
According to the rules, viewers can participate in more than one draw during the show, and Steam will automatically select a game that does not belong to you as a prize if you win. It is not entirely clear, from the wording on the home page, if you have to click on anything during the presentation to enter or if it is automatic, but the official rules suggest the latter. Hilariously, and presumably for legal reasons, you can also enter by sending a letter by mail to Valve.
As far as we know, the draw has not been officially announced yet. A post on ResetEra (which we noticed through PCGamesN) picked up the link to the list of games, which we assumed was launched before a later announcement. The list of prizes says "This raffle is already closed", but the rules clearly state that the raffle will be held during the show, so presumably it is only a placeholder. We will update this post if something changes, or if it turns out that these pages were posted wrongly in some way, but that would be surprising.
Valve also broadcast live our own PC Gaming Show at E3 earlier this year, and launched a raffle. this time he suggests that he is serious about becoming a bigger player in broadcasting live events. Just make sure to sign in to Steam while you watch if you want an opportunity in a game.