Turin Horse is apocalyptic because it centers around a father and his daughter and a half-dead horse, for the entirety of the film. They are (almost) alone in the world, and by the end we know there is nowhere to go but to stay in their stone house crushed by the wind, in the middle of a desert. It has clearly the signs of the end of the world. It is practically a fable, very basic and minimalistic.
Whereas
An Elephant Sitting Still is nested in reality, the reality of the society, with subcharacters, family, friends, colleagues, neighbours. It is based on the parable of the Elephant, but is very much grounded in real lives, interconnected, if often cross.
It is a severe criticism of Chinese society, but not as potent as say a Wang Bing (the decline of the industrialisation in
West of the Tracks, the rural workers who leave their children raising themselves to go search jobs in the city in
Three Sisters, the intellectual concentration camps in
Man from Nowhere) or Zhang Chi (
The Shaft; 2008) about the deathrate in a coal mine...
Except for the pointer to the eldery nursing home you mention, which is a precise pointer, I didn't feel like HU Bo was pointing finger at specific aspects of Chinese development (not the housing boom, not the unemployment, not the rich-poor gap. There are a few instances of stinking garbage, and the dirty river banks, but that's not specific to China.
But the fact the 4 protagonists believe in the Elephant story and wish to visit him, is a sign of hope.
There are 5 deaths in 24h (2 suicides, 1 accident, 1 dog, and one of old age), plus a gunshot wound : that's a lot for one day, and one movie (outside of Hollywood action movies), so the deck is stacked from the get go. It is difficult to overcome such piling up of bad news, especially for WEI Bu. And considering (he lost his best friend, a schoolmate, his grandma, his parents are horrible, his school is bound to be destroyed...), he's dealing with it pretty well during his journey, always on the move, trying to barter his train ticket, helping Jin, hopping on a coach...
YU Cheng, is a true nihillist, yet there is a glimpse of hope again in the scene where he saves the line cook from kitchen fire.
Cheng's ex-girlfriend seems well balanced and doesn't fall for Cheng's blame, she doesn't seem phased by their break up, and moves on. This is another character of hope in the film.
The scene with the shuttlecock (not badminton) is actually Jianzi shuttlecock, which is played with the feet (we see Bu play outside the coach with other passengers in the last shot of the film, with that very shuttlecock he stole from the group of old men). At the monkey pavillion, with Ling, he brags about his skills of juggling with his feet and Ling mocks him for hoping to earn a living, for both of them, with that.