yeah that's what people have been doing with pokémon for years! i guess getting past the kid blocking the path to mt. moon / skipping brock is that kind of thing
Yeah, and there are different ways you can go about it. Things like skipping Brock is called a sequence break, which means you're breaking the natural order in which you're supposed to do things. Which also has specific methods associated with it. Then there's other types of glitches, like getting yourself stuck into a wall being possible in a lot of early games because the programmers had to cut some corners in order to get good performance. They knew players would get themselves stuck in a wall at some point, so as a quick fix they usually eject you from the wall as quickly as possible, meaning it's a good way for speedrunners to save time.
Watching live memory can be very useful. So in some early FF games there's a glitch with regard to changing equipment in-battle. By figuring out how this affects the memory, and what the affected parts are used for, they were able to devise a way to teleport around the world map in FF2 and give characters super-powerful glitched jobs in FF3.
Unfortunately sequence breaking is practically impossible in FF2 because you literally can't go to later parts in the game without doing the earlier parts first.