I think the point of that moment is not so much that Gimli was in the chair, as the fact that somebody other than Denethor was in it, and the Throne is still empty.
Film does this kind of thing -- it uses visual cues to draw attention to iconic moments. Here, the most eye-catching person to be in the chair is Gimli (the disproportionate size makes us react to the sight as being a bit funny; the audacity of the Dwarf -- part of his character -- adds to our understanding of him). This was clearly staged by PJ to direct the audience's eyes to the fact that Gimli is there (as I recall the shot, it's just a bit to the right of centre, but still an in-focus background, with Gimli and the chair being framed by the debaters in the foreground -- we are supposed to look at him).
The point of this is, I think, two-fold. First, we see that Gimli has simply plunked himself down for a rest, which is all that this chair is good for now, since the King has come and the Steward is no longer needed. Gimli's presence in it changes the Steward's Chair into just another chair without a single word being said on the subject (the power of film). Second, we see one chair with a Dwarf in it, and another chair with no-one in it -- the Throne. Meanwhile, in the foreground, we have Aragorn, the guy who is now supposed to be on the Throne, or at least, who has the right to be, but who is most patently not sitting there. It raises the whole issue of sitting and who has the right to sit and why isn't Aragorn sitting -- in other words, it does visually what the book does through conversation between characters: Aragorn has returned, making the Seat of the Steward irrelevant (hence, it's now a comfy spot for a Dwarf); but he has not yet decided that the time is right to sit on his Throne, which remains empty.
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