The thing is the answer is excessively complex. Enough so that I figured nobody would read the entire essay if I included it.
In general, yes, the other intelligent competing species will have an effect, but only on the numbers of specific groups. They are already accounted for, to some degree, in the overall population densities. What must be kept in mind is that we can not just assign all of the "missing" population density to such creaures. If we did, they would suddenly become the local dominant races, and everyone else would be in trouble.
As an example, the population density of Keoland is around 10 per square mile. If we "fill up" the rest with 30 orcs per square mile, we suddenly have over 7 million orcs tromping about, and we need to find a way to explain why they aren't in charge of everything. Even adding monstrous predators at the same rate won't work, because the equivalent in manticores or whatever would still wind up eating the entire valley bare in short order.
So while it is reasonable to assume that the biosphere not taken up by humanoid population is filled by something, it is most likely that the vast majority of it is occupied by non-sentient animals that are reasonably able to be displaced by humans of stone age technology and above, rather than sentient races, monsters, or non-sentient animals and monsters that can neither be as easily displaced, or, worse, would pose an active counter-challenge for the space.
Demi-humans are, almost entirely, accounted for completely in the population densities I listed.
Humanoid populations are less included, but as they are in the fringe areas it should be remembered that those fringe areas can sustain signficantly lower populations to begin with. The high mountains of the Crystalmist-Hullfurnaces range and the spurs it throws off towards the Javan, are going to support fewer than 10 people square mile to start with. That will plummet precipitously with giants added in to the mix. In a sense, that "explains" why they raid so much. They are starving up there. Someone would have to calculate exactly how many square miles the Jotens cover, but I suspect the Steading of the Hill Giant Chief consumes from one-fourth to one-half of the available resources available to non-agriculturalists. It would be worse if people don't think hill giants are omnivores.
Finally, it should be noted that fantasy demographics in relation to subterranean creatures (the Underoerth/Underdark/whatever) absolutely require multiple "super" fungi and fungi feeders to function. I didn't get into that, and it would technically reduce the overall Sheldomar population density by at least 10%, as numbers of dwarves and gnomes and some halflings would be getting their food from down below, and thus not really count against surface population densities.
So, those are "some" thoughts. There is really a ton more than can be said on the subject, but as you get into more detail you require more technical knowledge, and lose the interest of more people. That's why I stopped where I did. If people want to consider more, I'm certainly game.