Also, the idea of being able to mimic the calculator is fun for kids. They like to be able to find an answer, and then check with the calculator (or REPL).
The advantage of lines is that you can spew out multiplication in the double-digit by double-digit range quite quickly. 51x23 for example is super easy to calculate - 10 100's + 17 10's + 3 1's. You're essentially just doing 50x20 + 503 + 201 + 1*3, but with lines to track everything.
Show it to a kid, and watch it blow their mind.
[1] http://lifehacker.com/5975917/quickly-multiply-big-numbers-t...
That doesn't sound like any kind of understanding is involved...
I sincerely hope that if this is used to teach children, they also properly explain multiplication rather than simply pulling a rabbit from a hat.
Maybe as they get older, it would be fun to present the line-crossing algorithm, and then ask them if they can explain why it works. My 7-year-old would not be able to do this, but she can easily relate to the multiplication-by-area analogy and its generalizations.