I think it might have been a short term thing, rather than an official "game of the month" addition. Might've been Curve that announced it via Twitter.
There's a NG+, and that's when you can use the cat plush. For different endings you need to not kill anything, keep healthy, and get through as quick as you can.
Not killing things is going to be tricky because I suspect you'll pretty much need to know the correct routes due to shortage of flares.
If I do NG+, can I still go for a better ending, or do I need to start a normal game instead?
I played the vast majority on the Vita, on and off over a few months, and then finished it off on the PS3.
I've still got the earlier save on the Vita so I befriended the cat on that save, and watered the plant. Having looked at the wiki, I don't think I can change the ending from where I am so I'll carry on slaughtering everything and finish again.
Protip - shoot the thinmen in the legs and you can run past them, also flares will disable fatties without killing them, and you can get more flares by trading bullets with The Director.
If you get a great pacifist run on NG+, there are two more secret endings on top of the main three (Blue: killed some things, Green: killed no things, Red: killed alll the things).