Interesting, I watched the same video and thought that it looked like a very easy swim through with lots of natural light and several exit points. Your perception is as valid as mine, it goes to show you how individual this issue is. But, a 'cave' as defined by consensus within the cave diving agencies has no natural light, meaning if you lose light you cannot see the direction to the exit at all, and/or a specific distance of combined depth and length to the exit, around 130-150 ft (I think) depending on the agency.
I think there are two fairly important, somewhat personal issues for recreational divers doing swim throughs like the one in the video. One, probably most important, is whether or not the diver is comfortable and confident in the swim through. Anxiety in a situation like that is not good...the other is, who are you in there with? Trusted buddies that could help diffuse a problem like an entanglement or a free flow? Or unknown divers that might start a real problem simply by freaking out, if for example another diver kicked off their mask by mistake.
Another thing to consider is, of course, the buoyancy control and swimming/finning ability of the people in the swim through. This has environmental implications too. And then there's the idea of gear configuration. It would generally suck to have to share air on a 30" hose in a swim through. Another example of the advantages of the recreational long hose.
I don't think that swim through (depending on depth, but it looked from the light to be pretty shallow) is anything like technical diving, but it definitely could be considered 'advanced' whatever that means. It does really come back to each diver knowing his/her own limits and taking responsibility for their dive decisions.