Steam free weekend game, how enter giveaway?

Can't.

Try joining a group or activating a game, then resync

EDIT : is it for Skullgirls ? It isn't in my library anymore but the store page still says I own it.

What game are you talking about in this case?
Sometimes the game stlll shows up in your "recently played games" and Valve's API will tell SG that you own it, even if you don't.

Yeah Steam is screwing us more and more each week. This weeks free weeekend started on Wednesday or so and probably will be the norm going forward

On the old SG site, someone told if you synced with the site before the start of the free weekend, it would work. Haven't tried on the new site, though...

You can't win my Skullgirls, back off. :D