As the title suggests, here is the way to get "400 Days" DLC for free on Steam.
This works for those people who bought the game via Telltale Store, got Steam keys when it was released, but are not eligible to get Steam DLC for free, but they need to download launcher from Telltale.
So, to play 400 Days via Steam you need to:
1. Install The Walking Dead via Steam.
2. Download your pre-order The Walking Dead launcher via Telltale website.
3. Install TWD from Telltale and after logging in for the first time, reset the game to get a download option for DLC.
4. Exit TWD downloaded via Telltale and launch Steam's TWD.
5. Go to episode chooser and you'll see 400 Days has been installed.
Now you can play 400 Days via Steam. I'm not sure if Steam achievements are working this way, but I know it syncs completely with your Steam save game and you can play it there, so as far as I'm concerned, all fine for me.
Hopefully this helped someone who had same wishes and problems as me.
P.S. One more time, getting "400 Days" DLC for free via Steam works only for people eligible for getting it for free because they've ordered the game via Telltale store!
UPDATE: STEAM ACHIEVEMENTS ARE WORKING!