As for the details about this story --
First of all, very few people could do push-ups for 30 minutes straight without breaks. At some point you reach simple "muscle failure" and simply can't do it anymore. Ask anyone who's done weight training at the gym. You do a certain number repetitions, and then you reach muscle failure. If you go hard enough, you can barely lift the empty bar anymore. No amount of will-power can make you do another rep. And there's no lasting damage from reaching muscle failure. That can cause the body to build more muscle for next time out. There are many fitness tests out there that make you do pushups to failure (how many can you do in a row?) This resourceful father was not only disciplining his boys, but developing fitness and stamina. I've known coaches (even to this day) who run their kids so hard they're almost throwing up. What doesn't kill you makes you stronger, as the saying goes.
Leaning against the wall with your forehead ... not that big of a deal. Just a more uncomfortable variant on standing in the corner. That's the entire point of punishment as a deterrent ... it SHOULD hurt some and be uncomfortable. If it doesn't, it's no deterrent at all.
Red mark on the chest? Big deal. No indication of it having turned black and blue (some tissue damage). You can get redness, with sensitive skin, from just a little push. If he had hauled off on the kid with his full might, the kid would have been hurt more than that. I had a teacher who used to regularly punch boys in the arm in class, hard enough that it hurt. But none of us minded. We actually felt like big guys when he did that. We liked it. It's like that old practice when kids used to get paddled, where the kid was supposed to respond: "Thank you, sir, may I have another?" It teaches you to take punishment like a man, with toughness, and while maintaining respect. Ladies do not understand this aspect of boys at all. Women personalize everything, whereas boys do NOT. Boys can get into a fist-fight and then go out an eat ice cream together five minutes later without any hard feelings. That's why the discipline of boys should be done by their fathers. Pax also made this point well in his post. At the same, time, however, I do feel that fathers should not administer corporal punishment to their girls (that should be left to their wives). Not that they have no right to; I just think it best not to ... to instill in them the notion that men should treat ladies with respect.
In the good old days, boys used to brag about taking a licking from their dad, almost as if it were a badge of honor, a testament to their toughness. They didn't wallow in effeminate "victimhood". Women/girls on the other hand, take it personally, and it's an emotional thing for them. But as long as the boy realizes that the father (or coach or other male authority figure) is doing it for their good, and with love, rather than just losing control ... the boy will actually RESPECT the toughness. Now these effeminate millennials all wallow in self-pity and victimhood. So this type of thing is also another chapter in the societal wussification of boys and men ... at the insistence of women. That's why boys who are raised by single mothers or "sensitive" fathers, turn into effeminate wussies.
Eating soap (presumably for bad language or talking back). How much soap was forced to be ingested? Five bars or just a relatively-small shaving. Did this "eating" mean that they were forced to actually swallow and ingest it? Even then, how much?
Most of this sounds like a total crock. Burns, broken bones, open wounds, lots of black-and-blue marks, enough soap eaten (of the right kind) to cause poisoning. Sure, that's abuse. But what's described here is a joke.
Then someone asked: Who turned the guy in? Was it a wife who doesn't like him using it for leverage in a planned divorce (as she's having an affair)? I actually know a couple women who did exactly that. Was it the kids? Did they call the cops? Did they report him at their school? Or did the kids just talk at school and get overheard by some busy-body teacher. Maybe the boys didn't even mind but were almost bragging about it to their friends. "Yeah, I got busted [doing this or that], and my dad made me do pushups for half an hour." Have we turned this into a child- and female- run police state? I've actually heard of kids threatening their parents with calling the cops if they tried to spank them ... completely undermining the parents' ability to discipline them.