I don't think so. A = fired employees. B = unpleasant players. B is contained within A, so B implies A ("Toxic players tended to be toxic employees") but not the reverse.
It could totally be that all non-fired employees are toxic, and viciously went after their weaker colleagues by having them fired! I guess that would make them toxic, but whatever.
Maybe Ted for fired for sexual harassment of a co-worker. Maybe he worked for HR and rarely, if ever, played LoL in the first place. He'd be fired as a toxic employee without anything in his LoL chat log to hint at it.
What they're saying is that if you have a toxic LoL chat log, you're likely to be a Ted. But the reverse isn't true: you can have a pristine chat log, and still be a Ted.