So this is a category error much like saying French is not a type of poodle. I assure you, it is, just as, well, two can play at this game https://en.wikipedia.org/wiki/Trappist_beer .
The link you posted shows the opposite: Trappists brew many types of beer, though arguably Trippels are the most common lately.
Saying Trappist is a type of beer is like saying French is a type of poodle — if you used the label only to refer to a poodle bred in France.
A more apt comparison is saying Bordeaux is a type of wine. Bordeaux is a region in France; it is well-known for 5-6 types of wine; any Bordeaux wine that qualifies for AOC proudly displays its Bordeaux heritage on the bottle.
Which raises the question[0], "Why French poodle?" Is there a non-French variety? Wikipedia indicates not [1], although they probably originated in Germany. [2]
[0] Not "begs". Never "begs the question," even if I am being pompously pedantic. [0']
[2] Also, while the Germans refer to the breed as "Pudel," the French call them "Caniche". So of course in English we call them <"French"> <German word>.
There are category category errors being committed on all sides. The confusion is arising from the word "type". To some, a "type" of beer is a style of beer characterised by common ingredients, methods and appearance. To others a "type" of beer may be as loosely defined as simply the kind of container it is stored in (can, bottle, draught).
Saying Trappist is a type of beer is like saying French is a type of poodle — if you used the label only to refer to a poodle bred in France.
A more apt comparison is saying Bordeaux is a type of wine. Bordeaux is a region in France; it is well-known for 5-6 types of wine; any Bordeaux wine that qualifies for AOC proudly displays its Bordeaux heritage on the bottle.