Update: Valve has officially announced the giveaway. Here's how it'll work: "Each logged in, non-limited Steam account will receive one entry per draw while watching the broadcast [on Steam]. Steam will randomly choose 150 lucky winners from eligible participants every 15 minutes. Each winner will receive a game they do not own from the remaining prizes." The draws will run for the full broadcast. Original story follows below.
If you're watching The Game Awards tonight, you may want to watch on Steam, or at least have the stream open on Steam. If you do, you'll apparently have a chance to win a free copy of a nominated game—so, a bunch of the best games of the year, including Divinity: Original Sin 2 and XCOM 2 plus the War of the Chosen DLC. You can see the full list of prizes here.
According to the rules, viewers can participate in more than one drawing throughout the show, and Steam will auto-select a game you don't own as the prize if you win. It's not entirely clear from the wording on the main page whether you have to click anything during the show to enter or if it's automatic, but the official rules suggest the latter. Hilariously, and presumably for legal reasons, you can also enter by mailing a letter to Valve.
The giveaway hasn't been officially announced yet as far as we can tell. A post on ResetEra (which we noticed via PCGamesN) picked up the link to the list of games, which we assume went live ahead of a planned announcement later today. The prize list says "This giveaway is now closed," but the rules clearly state that the giveaway will take place during the show—so that's presumably just a placeholder. We'll update this post if anything changes, or if it turns out these pages were somehow posted erroneously, but that would be surprising.
Valve also livestreamed our own PC Gaming Show at E3 earlier this year, and throwing in a giveaway this time suggests it's serious about becoming a bigger player in live event streaming. Just make sure you're logged into Steam while you watch if you want a chance at a game.