Hey Milu,
The "Imperial/Double Red Ale" category is a relatively recent creation and to me shares some similarities with the Barleywine and Strong Ale categories, but if I were to choose at the moment, I see BB Red as more of a Strong Ale. The Strong Ale category is like a "catch all" to beers over 7% ABV that don't exactly fit under the guidelines of traditonal styles. The best American example to this is the famous
Arrogant Bastard Ale (at 7.2% ABV); it could be an amber ale, it could be an IPA, but that beer doesn't fit neatly into either category, so it's accepted as a Strong Ale.
I think that if the "Imperial/Double Red Ale" category were more widespread, then I think we would see such style implemented on BeerAdvocate/Brejas/RateBeer. It could happen in the near future; the "Black IPA/Cascadian Dark Ale/India Dark Ale" (whatever you want to call it) recently became a recognized style after it became popularized. As of 20 years ago, there was no such thing as an "Imperial/Double IPA", but as it became popular 10 years ago, such style became recognized.
I think the reason why we see "Pumpkin Ale" and "Quadruppel" on BeerAdvocate is that those styles have accepted guidelines (at least in the US), even if they're not official styles. In my opinion, there are still a lot of questions up in the air to what makes a Double Red; there are no concrete guidelines yet. Many of the Double Red's in the US are that in name only; the famous
Nugget Nectar calls itself an Imperial Amber, but most consumers see it as either an IPA or a "regular" amber ale. More recently, an American brewer renamed and remarketed one of its beers; it used to be called
Gordon and was marketed as a Double IPA, but the thread of a lawsuit changed its name to
G'Knight, and now it's marketed as an Imperial Red Ale, even though the beer itself is the same!
I hope that I answered your questions Milu. And yes, I do have a bottle of Baden Baden Red Ale in my house, so now I'll be more interested in re-tasting it