Maybe I'm parsing this wrong,
seems like, or ignoring a distinction...
but it looks awfully like the author meant to imply an actual leader, not just "Leader role from 4e." 'Cause otherwise he would have said that, right?
I think we need to clarify something, here, though I just said it up thread, it may have been too brief or off-handed.
There are two senses of leader that apply to the warlord, legitimately, as contrasted to the unacceptable senses of class choice dictating party leadership/superiority/authority in the fiction or conferring the privilege of bossing fellow players around at the table.
One, is the 4e Leader role, which /explicitly/ denies the objectionable senses.
The other is conceptual: the warlord has leadership skills, in the PH1, either Tactical or Inspirational, beyond the ordinary. Which is independent of the objectionable senses.
The ability to inspire or see tactical opportunity is of great utility to a leader, but one can be in a superior social position of formal leadership and authority without an iota of either, or at the bottom of the social pyramid with a surfeit of both. The former case can be disastrous (or not), the latter, those potentials can languish unless there are willing equals or even social superiors able to recognize and take advantage of them.
Maybe not the formal leader of the party in the sense that they get to make the decisions and other players have to obey
Formal leader in a superior position, though, is the sense you're objecting to. Battle-leader clearly limits it to combat, not really problematic, and tactical or inspiring to the abilities of the original PH1 version. It's a brief, but not unreasonable, beginning if an explanation of the class (obviously, selectively quoted out of context, to maximize the impression you were searching for - actually, it's amazing that's all you could come up with, ENWarlord fans must have fewer bad eggs than I thought).
Keep looking, but in the interest of not bringing on a zombie-warlord-apocalypse of thread necromancy, maybe not so far back?
But certainly somebody who derives their powers from leadership, whether through brilliance or inspiration.
As a martial class, the Warlord derived it's abilities from martial ability, the talents and skills - not the position or authority - of leadership.
When people say "But any class could be a leader," that's mainly true in the objectionable sense of the arrogant Noble or bossy player - taking up the position, without the mechanical support.
