At the end, the filmmakers acknowledge the family for their cooperation, so I assume they didn't go as hard on them because of that

His father was alcoholic, emotionally and physically abusive to his wives (he had 2) and children. That was the reason he took off
That's correct, but to clarify: the father was physically abusive to both wives, frequently in front of the children. There's no indication that he was ever physically abusive to the kids, but beating up on their mothers in front of them constituted emotional abuse of the first order. Chris's sisters from his marriage to Marcia confirm that they were terrified the father would beat them next.
He never did, but causing them to live in fear was abuse.

His father was alcoholic, emotionally and physically abusive to his wives (he had 2) and children. That was the reason he took off. It didn't become public info until his sisters came out and told the story. Sean Penn knew something about it but needed to have the cooperation of the parents. The sisters said Chris' mother was a victim of frequent physical abuse. But when a documentary was made, both the father and the mother denied that there was ever abuse. I believe the sisters.

The wife in this movie isn't technically his wife, as he was still legally married to his first wife,
Not true. He was legally married to Billie, but not when Christopher was born. He ran off with his assistant, leaving his first wife, and the divorce took a couple years to finalize. By the time shown in the movie they had been legally married for many years. They still are.

His dad was a horrible douchebag who valued material things over anything else.
The wife in this movie isn't technically his wife, as he was still legally married to his first wife, with whom he had children that he didn't see. Chris finds this out when he's a teenager (16 or so?) and finds it very hard to accept that his parents lied to him and his sister their entire lives.

There is more detail in the book about his family. Seems he resented his father because he had an affair and left his other family for his assistant, which is the fathers current wife in the film. It's been a while since I read the book, but it's along those lines.
It's easy to be a rebel and be independent etc. when you are 100% sure that no matter how bad it goes or you screw up, you can always fall back on wealthy loving parents. He did what he did because of the hubris of youth, spoiled kid who thought he'd figured out something new, he was a walking clich. Most live to outgrow the phase and realize the folly, unfortunately he never got the chance.
I don't judge his actions as harshly as many on this board, yes, he was ultimately responsible for his own demise. It could have been any of us at that phase of life, maybe not starving in the woods but something else, like wrapping a car around a tree etc.
"if it was any good they'd have made an American version by now." Hank Hill

"He was a spoiled upper-middle-class white kid. He had no other major things in life holding him down - nothing to overcome.
He had the luxury of being able to resent himself and who and where he'd come from. "
This.
brb parents offering to pay for HARVARD LAW SCHOOL but running away because they don't love me.
Please

The movie says his dad/mom verbally and physically abused each other in front of the kids. That's no joke.

I am not entirely sure, but I came across a website which is the main site behind the real story, not related to the film, and the sister of Christopher wrote a blog type piece describing what their life was like, and one of her points was that the film didn't tell the whole story of everything going on at home, suggesting it was worse than implied.

In real life what did Chris' parents do to him??

I'm not so sure. I think the fact he and his family had all of this wealth and comfort, however were still unhappy, especially his parents and the way they fought all of the time, made him question what is happiness, and how do you find it.

He was a spoiled upper-middle-class white kid. He had no other major things in life holding him down - nothing to overcome.
He had the luxury of being able to resent himself and who and where he'd come from.
I think that he'd have done the exact same things if his parents hadn't been the way the were. Maybe would've written them, though.

I believe that the film didn't include a lot of the 'goings on' within the family out of respect for the parents, as they felt it would be un-necessary to include very personal family information.

I agree, and I didn't like him at all in the movie at the beginning. But at least in the movie, they made him more open-minded but still keeping to his personal code as time went on.