Are “Mexican Stouts” actually Chile Beers?

Depends. If the focus of the beer is the addition of chile peppers, then Chile Beer (typically pale lagers and ales). If it's just one of several ingredients, drop it in American Imperial Stout.

 

There's no easy answer for this. Is there a category for "Orange beer" for all beers involving orange? Fruit and field hardly suffices; it's not specific enough, and that style doesn't include lambics, milkshake IPAs, et al ...

I'm with @Todd in that it depends on the nature of the beer. I think in most cases, a stout with chilies is going to be classified as a stout. It's a stout with chilies, no different than a stout with chocolate, vanilla, or coffee (which do not have their own sub-styles).

When chili peppers are the clear focus of the beer, that is when I see the classification going in that direction. Further, chili beers aren't specific to brewing technique; they can be lagers, pale ales, dark ales, stouts, and anything else. There are plenty of chili pepper beers where that's the obvious focus, and the malt/hop/yeast combination is merely the palette used to show them off. That is a chili beer.

So no, I don't think the mere inclusion of chili peppers in a beer necessitates it being classified as a chili beer. Not only would that reclassify a ton of classic beers in a way that doesn't really make sense (in particular many famous imperial stouts that would now be ... not stouts???), but again, it implies that if you add one ingredient, it changes the classification of the beer. Not only do we not have sub-styles for every possible additional ingredient, it would make classification literally impossible when you have more than one of those ingredients - and there's no reason that chili is a default classifying ingredient over any other additive, much less the malt base and brewing technique itself. Go ahead and classify Prairie Bomb! or Huna using that logic. They're either stouts, or they're absolutely unable to be classified at all.

 

Many of the “Mexican Stouts” that you would describe contain chiles as just one of many added ingredients to the beer and are not specifically the focus. In that case, I would classify these are Imperial Stouts.

When chiles are the only added ingredient or are the focus of the beer, then I would classify as a Chile Beer.