It all depends on how you define support. I'm sure Microsoft will be selling 360 hardware for another year or so, but considering almost all of it's library is out and MS makes a killing on LIVE subscriptions, that's not really support. It's milking a dead cow.
Personally, I consider support to be the last notable release (has a target fanbase) which will not be part of the next generation's library, so yes, I will consider third party support. Dark Souls 2 and Lightning Returns are pretty much the last of the generation; I can't immediately think of an upcoming title not on PS4/ X1 which I would even call AA.
That's not nine years. That's a notch more than eight on a quite successful console.
I think it's fair to say the X1 might have a ten year cycle, perhaps longer, except that X1 and Wii U sales aren't that good. It's my guess that Nintendo will pull the plug on the Wii U in two or three years to go all-in on a 3DS successor. If Microsoft hasn't turned the X1 around by then, they may pull the plug, too, shortly thereafter.