I'm not a parent, but I have observed Japanese parents with young children and they tend to recognize that 2 year olds are not really responsible for many of their actions. Maybe he lost his grip on the toy, maybe he didn't understand that the car can't catch it or doesn't like having things thrown at it. They tend not to shout anyway, and I've noticed that Japanese children tend to be a lot quieter and calmer which may be related.
Instead they will calmly explain that the cat doesn't like that. Play stops, the child is faced with their parent and even if they don't understand exactly what is being said they understand the tone of voice and facial expressions. They might try to explain that only dogs like to catch things, making it a teachable moment.
So, kinda like what you do but without the need for shouting and time-out. I see the logic - punishing a 2 year old for not understanding seems somewhat unreasonable, since being a 2 year old you can't really expect them to have understood. For repeated behaviour it goes to loss of privileges, like taking the toy away.
It seems to work pretty well. Japanese kids seem quite mature, and some of the toys they get are kinda surprising for a westerner... Fairly sharp woodworking tools, for example. I dunno, I'm not an expert, but I think I'd like to at least understand what they are saying before making a judgement and unfortunately TFA doesn't really explain it, as you pointed out.