Q:

Japanese Multiplication: 日本の掛け算

Is  the Japanese Multiplication really a thing or a joke? How does it work?

Here is the video on youtube https://www.youtube.com/watch?v=JVgnUMdM6ME

A:

It's essentially a visual way to expand the product :
\begin{align}21\times 23 & =(2\times 10+1)\times (2\times 10+3)\\ & =(2\times 2)\times 100 +(2\times3+1\times 2)\times 10+1\times 3\\ & = 4\times 100+8\times 10+3=483.\end{align}
Later in the video you see that with $14$ points, the $1$ is crossed and added to the next number; that's simply reporting the tens to the next power of $10$ like you would report a number in the "usual" way to do written arithmetic.

