Clicking on the picture brings me to the store page for a game that was released on May 10th, 2018. If this is the game this giveaway is for, then it isn't the free game (I know I have the free game, but it doesn't show up as Desire in my Library, it shows up with a different name that I cannot recall at the moment).

The free game (well, the one that was free at one point) is a Visual Novel I believe, while this one is a Point & Click.

If that is indeed the case, you may be thinking of the other game with the same name, and you may not have this particular game.

Désiré (2016) and Desire (2018) are two separate games.

Désiré (2016) and Desire (2018) are two separate games.

Not exactly. The game is still there, in every library of every person who's got this game earlier. It's still playable. But yes, for a new version to be visible a replacement is required.

You need to search "sir" and it'll find it.
And yeah, my 2016 copy was fine and dandy.

Happy cake day ;)