Short ribs cut the way you described in italics are a little tricky to do yourself. You have to get "English" cut ribs sawn in half (or do it yourself), then you make an "open book" "butterfly" about 3/4 of the way down to the bone, and continue opening it about 1/4" thick, and rolling to the next cut. When you've got the thick side done, you open the other side at the cartilage, then trim the cartilage off the bone. PITA!
I'm not quite sure that's THE traditional cut for galbi or not. Most everything I know about Korean food I learned here in SoCal (which is a pretty good place to learn it). There are so many Koreans and so many Korean restaurants here, I think you get a fairly representative sample; and that cut is not only dominant, it's not the most common in soon-tofu houses, AYCE barbecues, generic Korean restaurants, you name it. Here, anyway, "LA galbi," a thin flanken, is so common you might even call it dominant. But even the very tradtional places don't usually go through the process of successive butterflying.
Is LA typical of Korea? Of some Korean regional cuisine? I can't say -- don't know enough about it. But given that there's something like 1/2 million Koreans in greater SoCal -- about twice the number of total Koreans living in the rest of the US -- one would think it's fairly representative.
On the other hand, that they call the most common style of cutting "LA galbi" has to mean something.
Anyway galbi is not the only Korean use for shortribs, and you see a lot of (what would otherwise be) English cut, boned-out. And, as I said before, you see that cut in all the meat cases in Korean neighborhood, but not too much anywhere else. I think it gets used for galbi, bulgogi, bi-bim-bap and other things as well.