A lot of big cats suffocate their prey. Just clamp down on the windpipe and wait.
I found myself at first rooting for the lions, 'cos, you know they can’t just go to the supermarket to PURCHASE their needed food. And then for the buffalo for taking a stand and getting away. Never voted for the crocodile though.
Heh, Buffalo 1
Lions 0
Croc 0
On the news, after showing the video, they interviewed the guide and the guy who took the video. The guide said he looked all over the area to see if there was a corpse of the calf, or bones, etc. There was not, so he opined it must have survived. He said in all his years as a guide, he never saw anything like that.
The older guy who took the video was asked if he was an expert with cameras, and he said he only used the thing about once a year, and had to check what buttons to push. Considering that, he should win an award.
AIUI, when many of the large cats immobilize their prey, without having already dealt it a death wound - they are usually asphyxiators - they clamp about the animal’s windpipe, and suffocate it. So, while the buffalo calf wasn’t exactly happy where it was, it was also quite rescuable.
Wow. Just, wow. I always get sad watching predators take down their prey on nature shows, and console myself by reminding myself that’s the way it is out there. Nice to know that sometimes the prey fights back and wins as well, with absolutely no intervention from humans. Go buffalos! 
Before you go thinking that the buffalo in the vid were really analogous with cattle, or even Bison - Cape Buffalo have a certain reputation. They are regarded as one of the most dangerous animals on the continent, and have been known to take out hunters gunning for them.
I was rooting for the lions the whole time. How come everyone sees the buffalo as the underdog here? They had the advantage in both numbers and size; they could have trampled the whole pride of lions to death.
In that case, I’m going to feel sorry for the crocs - for them, it must have been like seeing your lottery numbers come up, then realising you didn’t buy a ticket this week.
There’s also another technique lions use where they grab the prey by the muzzle so its mouth and nose is inside the lion’s mouth, and it can’t breathe. Again, it takes time to die that way.
I too was cheering for the lionesses (I don’t think there were any boys there - the girls do all the hunting, as far as I know). I could see all their ribs, and chances are good that they are nursing cubs. Oh well. Circle of life and all that.