That's like saying hamburgers are allowed, you just can't have any ground beef in them. Haggis is made from sheep's lung - that's what it is. They just do a phony version for the Americans and call it haggis anyway.
The Wikipedia page also references a 1615 recipe for haggis which does not require sheep lungs, saying "oat-meale mixed with blood, and the Liver of either Sheepe, Calfe or Swine, maketh that pudding which is called the Haggas or Haggus".
To me this sounds like the old gatekeeper question of who gets to assign authenticity. Since things called "haggis" are sold in Scotland (or at least the UK), and do not have sheep lungs, I think that means it is incorrect to say that just because a product sold in the US or Canada does not have sheep lungs in it, it cannot be called haggis.
I do not agree with your analogy. People do refer to "vegetarian hamburgers". For examples, https://www.yummly.com/recipe/Vegetarian-Hamburgers-626992?p... and https://www.tripadvisor.com/ShowUserReviews-g30196-d10434055... .
People also refer to vegetarian haggis - https://www.hendersonsofedinburgh.co.uk/food/vegan-haggis-an... and https://www.macsween.co.uk/products/delicious-every-day-vege... .
The Wikipedia page points out that "Some commercial haggis is largely made from pig, rather than sheep, offal" and points to http://www.ramsayofcarluke.co.uk/products/traditional-ball-h... which uses pig lungs instead of sheep lungs.
The Wikipedia page also references a 1615 recipe for haggis which does not require sheep lungs, saying "oat-meale mixed with blood, and the Liver of either Sheepe, Calfe or Swine, maketh that pudding which is called the Haggas or Haggus".
To me this sounds like the old gatekeeper question of who gets to assign authenticity. Since things called "haggis" are sold in Scotland (or at least the UK), and do not have sheep lungs, I think that means it is incorrect to say that just because a product sold in the US or Canada does not have sheep lungs in it, it cannot be called haggis.