No, it is free forever. Just add it to your game library on shop page before the offer ends (no need to install it). It is not a "free weekend game" (I guess you think of this).
I still would say so if I read this:
"Spielen Sie Amnesia: The Dark Descent gratis bis Mittwoch um 19 Uhr MEZ! "
It says "play for free until ... " and not "get it for free until ..." but maybe you have already tried it and I am dead wrong here?
Midweek Madness - Amnesia and Penumbra series, 80% Off!
Announcement - Valve
Save 80% on Amnesia and Penumbra series during this week's Midweek Madness*!
Additionally, grab a completely free copy of Amnesia: The Dark Descent on Steam until Wednesday at 10AM Pacific time! http://store.steampowered.com/app/57300
*Offer ends Friday at 10AM Pacific Time
And on the shop page:
MIDWEEK MADNESS SALE - FREE copy of Amnesia: The Dark Descent!
To help you prepare yourself for the imminent release of SOMA, we have decided to have a sale with an 80% discount on all our previous games. Hurry and you’ll get Amnesia: The Dark Descent for free during the next 24 hours and the game will remain in your library forever.
If you pre-order SOMA you’ll get a 10% discount and you’ll be able to preload the game starting tonight.