There are subclassifications within the “Generation X” grouping that address the skater/extreme crowd. The most commons classifications I’ve seen are Atari Gen-X and Nintendo Gen-X. I’m a child of the 8-bit generation, BTW.
Those youngins are included, though, because there are still unifying cultural elements between someone who was born in 1966 and 1976, the most dominant being MTV and home computers IMHO. Because I grew up in a place that was culturally insular and somewhat behind the times, I tend to identify with very late baby boomers. Popular culture among teenagers in Buffalo during the early 1980s resembled what was seen in Dazed and Confused or Detroit Rock City more so than the Chicago North Shore/Molly Ringwald/brat pack films of that day. which supposedly scream Atari Gen-Xer to most now.
I actually did a paper about this back in grad school, and found the earliest reference to “Generation X” way back in 1964. It was the title of a book by two British journalists containing portraits of teenagers of their day. In other words, it described the front end of what we now call boomers. So the term has been around for a while, but it didn’t seem to “stick” until it got to its current meaning.