Let me twist this question around.
Find me people that know about a trackball and it's advantages.
Are these people winning on a competitive level in Starcraft, Warcraft III, BattleField, Call of Duty, or whatever hot multiplayer game people are playing nowadays that they themselves play?
I don't see how a person can play Starcraft or Warcraft with that thing.
What types of genres are trackballs good for? and what type are they bad for?
What exactly do you mean, "find me people that know about a trackball and it's advantages"? You're in a thread full of them. I also linked you to a few more.
As far as competitive gaming goes: I have absolutely no clue. None. I'm not the right person to ask. Personally I'm not a competitive gamer... nor do I have a lot of skill. That said, I'm still pretty good; I've been in full 64-player games of BF3 where I sit at the top of the scoreboard (though that's rare). More often than that, I can usually at least maintain a K/D of 2:1. So I can confidently say that I'm decent.
You might respond "Well, then maybe trackballs aren't that great after all;" but that's a null argument because you could switch me back to a traditional mouse and not much would change. I've played a ton with both, so I'm pretty used to both. My skill mostly depends on me, and not my input method.
That said, there's still reasons why I prefer my trackball. Comfort and ease-of-use is one of them (no arm or wrist movements when gaming, no cramps). The best feature, however, is the infinite range of movement.
With a traditional mouse you're forced to pick up or "row" your hand. It doesn't matter how big your mouse pad is, or how high you have the sensitivity cranked up: You still have to row your mouse. Period. You're limited to the size of your desk. Your range of movement is restricted and finite. With a trackball, I am not bound by these restrictions.
I can move the mouse cursor infinitely in any direction using only the muscles in my fingers. At no point do I have to pause and lift up my mouse to "reset" it's position. Because of this there is fluid, uninterrupted movement. (As an aside, sometimes my teammates in TF2 laugh at me because I can make my character spin around in circles at a million miles per hour, so I look like a blur.
Totally useless, but it's just me demonstrating how fast I can move my cursor).
But like I said: These differences could be negligible to those who've grown up using a traditional mouse (which is understandable; you've been using that kind of mouse for you entire life, so it's completely hard-wired into your brain). Most of my friends refuse to try trackballs because they'd essentially have to "re-learn" how to interact with their computer after years of doing it another way. And that's absolutely fine. Personal preference.
With all due respect to competitive/pro gamers, their reasons for not using trackballs are probably the same as I mentioned before:
1) General ignorance
2) No desire/Not enough good reason to switch (Competitive gamers are so trained and neck-deep in their own sport, are they gonna take a month off to learn a new input method? Probably not)
3) They're 100% comfortable with what they got, so they don't care in the first place. Which, again, is totally fine.
As far as what games trackballs are good for: All of them. There's nothing you can do with a traditional mouse that you can't do with a trackball. The only exception would be the Trackman Marble, which is the one I linked you to above. It doesn't have a scroll wheel, so in games like RTSs that make heavy use of one, you'd have to use the secondary buttons on that mouse to scroll, or use some other method. I have "scroll keys" on my Logitech G105 keyboard in case I need them, so that's what I use.
I think I'm in the minority though. Most trackball users seem to be using the M570 and it's variants. That one has a scrollwheel just like any other mouse.
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