The announcement appeared on the Don't Starve Together website after solving a puzzle: you had to interact with a tuning fork in the room and enter a code that opens a portal. An alternative is to simply follow the link to the website, where the logo is hidden by fog.
Some speculated that the teaser concerned a mobile port or the Newhome game from Tencent, but the developer confirmed on the Don't Starve server that it is a new internal Klei project.
I want to clarify that this is a new game. If you knew about it before the link on the ARG site, this is not it. Also, this is not a mobile Don't Starve. The page states: this is a new game.
So far, fans are building theories: from a roguelike spin-off to Don't Starve 3 or a remaster of the original. Some are even joking about a karting game. There are no clues other than the ARG page, so everything remains a mystery for now.