This is interesting because it counters the idea that someone has to be a jerk to get ahead. However I'm also not sure the study really examined the idea too well, and ended up feeling like it's the sort of thing that could be misinterpreted and overleveraged.
In my personal experience (which is limited) there's a certain constellation of organizational characteristics that leads to disagreeable individuals attaining power, and organizational "combativeness" isn't really it. I think "corruption" is closer, and good luck measuring that with a self report survey.
Then again, maybe the relevant issue isn't whether or not people who are jerks are more likely to attain power, it's than once they're there they're more likely to cause problems, and they're not less likely to attain power. So then them being in power is salient.
But then I think you have to ask, why aren't they less likely to attain power? Is this a case where a zero correlation is actually masking some mixture of processes, one positive in direction and the other negative? If so you'd think that certain settings would inhibit one or the other of those processes.
I guess I feel like this is a case where studying normative organizational dynamics in a cursory way could end up being really misleading.