1. Triangle chokes came from Judo, and in Judo it was considered a sport technique.
Sure. You do know that Hatsumi held a Yondan in Judo, yeah? And that most of the senior members of the Bujinkan are also old Judoka themselves? And that the instructor bios on the website cite ground fighting (including one instructor they refer to as their "specialist" in the area), and BJJ in the background of at least two out of the four?
MMA and Bjj pushed its self defense aspects in modern times.
BJJ, I'll give you… MMA pushing a "self defence" approach? Not so much… I'd also suggest that they're more artificially transferring it across to their approximation of self defence methodologies, but that's getting into a different area entirely…
Interesting seeing a Koryu style using it.
What Koryu "style" do you think you see using it?
2. The Triangle or potential arm bar shown here is pretty much a lost cause. The person doing the choking is ripe for getting his neck hyper-extended by his opponent simply walking forward, or getting picked up and slammed.
Hmm… the guy on top has his body pretty well compromised… there's more danger of him overbalancing and falling forwards than walking, or picking the guy underneath up (not enough strength with the back in that position)… and as far as walking forward, that would put more pressure on the back of the neck, so also not particularly likely. His most likely escape is really to back out… which is certainly possible, due to the poor positioning (stacking up) of the guy underneath. That said, we don't know when exactly this photo was taken (in a sequence), it could be part of a live (resisted) drill or sparring exercise (of a kind), so I don't know that it's supposed to be an example of a finished action. For all we know, he was going for a triangle, the guy started to shift back, and he's about to transition into a sweep… it's what I'd be looking to do there…
I find it interesting that they would use this image to advertise their school.
Maybe they just really liked the photo? Maybe they thought it captured the chaos of combat? Maybe it showed the instructors face, but not the students (similar to a photo on my schools Facebook page, chosen for similar reasons), which is what they wanted? Maybe they weren't concerned with showing absolutely perfect technique, but more an idea of some of the things covered in their lessons?
Maybe they realise that not everyone visiting their site will be looking for technical perfection in each image? After all, is every photo on every BJJ site an image of perfect technique, or do you think that there might be some with some flaws, or some that are not "technical", due to being transitional moments?