I love westerns very much. I have seen a few hundred so far, almost none of which I didn't enjoy. So I'd say I've seen many great westerns and do love the genre.
As far as parameters go, I think it's generally difficult determining what constitues a genre, and even more so what doesn't. For me it's probably something like this: if a film has enough elements of a genre in it, Iwould count it as belonging to that genre - even if the film has more elements of other genres beside the one I'm interested in. Generally I think genre itself is something that is constantly changing, not just through new films, but also through the discovery of old films and especially new "views" on older films, so to speak. So there are always many fluctuations, and new genres emerging, and while many prominent genres usually have quite a solid core, the edges of this conceptual model are not solid at all. Genre is very much a construct, something that keeps growing and changing and is hard to pin down in every case. One important thing imo, is also surely the fact that most films are located in several genres at the same time (or at least 2), and it is very very difficult to find a film that belongs only to one genre (I can't think of one from the top of my head). Regarding westerns, I think it's difficult to find one that isn't at the same time an action film, or a drama, or a comedy, to list only the most prominent examples.
I hope this explains my position a bit. Also, when I compiled the Top 20 (which took a while), I didn't try to think of typical westerns and then list the 20 that come to my mind, but I took a different approach, in that I went through all my favorite films from any country and any genre, than picked out the US films, and then picked out the films I would consider a western, and then reduce it to the 20 I love the most. The result was very surprising for me also! Some of the films on the final list I hadn't regarded as westerns before, but simply because I hadn't thought about it. The Chaplin film for example, was just a Chaplin film so far (Chaplin is also my absolute favorite director), of course a comedy, but I hadn't given it any thought regarding genre before. But of course it is set in the wild west, during the gold rush, so it's a typical western in this regard, and when I recalled some scenes from it, there were so many western elements in them.
Maybe most of us, when we think of a genre, we usually start with the most typical films, and then we think about films that are similar to the most typical films. But nowadays I think this approach is flawed, as it has one big problem: it solely focuses on the core elements, and disregards the fringes, meaning: Why not try it the other way, and see what minimum criteria a film has to fulfill in order to be part of a genre in one's opinion? Is this a less valid approach? I don't think so. Thus with going by the approach of "is this a western?" instead of "is this a typical western?" I was able to surprise myself, when I found out that some films I hadn't thought of before as westerns I actually regarded as westerns, after I questioned them. I like this approach, because it also seems to broaden the core of a genre and makes you realize how genres come to exist in the first place and how alive this terminology actually is.
EDIT: And of course as we all know there are many different kinds of westerns, e.g. revenge films, Civil war films, films about Indians, about settlers, about father-son conflicts, about political themes, about the western myth itself, etc.pp.