Caution: I am not a biologist and my opinion is only that of a barely educated layman... But since you asked, herewith MY thoughts.
The four hazards are:
viruses: 0.01 micron
bacteria: 0.3 - 1 micron
protozoa: 3 - 20 micron
chemicals: farm, pollution, you name it, and not handled by any of this.
When water contains lots of organic matter whatever chemical you are using may be partly used up on 'dead' organic matter like tannins, bits of silt, moss, etc. So you may need to increase the amount you use, and predicting how much is 'not easy'. It can make the water taste quite yuk.
One solution to this, which also has some visual appeal, is to filter the water first with a coarse filter, as demonstrated on the video. I have even use a handkerchief at times ... What you usually don't know is where the threshold of your coarse filter is, but you should assume that it could let even protozoa through, unless you have certified evidence to the contrary.
Now, the bag filter material used in the video is NOT rated for human/medical use. It may be rated at 1 micron, but the first problem is we don't know what that means. What I can tell you is that the rating does NOT mean that the filter will block everything below 1 micron: it won't. It is a statistical filter. It might block 90% of the materials below 1 micron, ON AVERAGE.
The second thing we don't know is whether every square millimetre of the fabric has the same effectiveness. It is entirely possible that there could be weak spots in the fabric, places where it only filters to 5 microns. The manufacturing process used does not guarantee perfect uniformity. It is not designed for that.
So what comes out of all this is that the filter should remove all 'large' organic matter, and probably most protozoa as well. It will not remove chemicals, viruses or bacteria, and it will possibly allow a small percentage of protozoa through. However, the concentration of protozoa in water is never large, and you need at least 10 cysts for Giardia to be a hazard anyhow, so that might make most water *effectively* protozoa-free.
That leaves you to treat the water with a chemical and wait maybe only 10 - 30 minutes, depending on the water temperature. I'll stick my neck out here and say that in most cases that would be safe enough. There are a couple of places where I know Giardia is a serious hazard, and in those places I would hesitate, but elsewhere it would seem pretty safe.
A thought worth considering is that I think the pleated filter in the Katadyn Hiker uses a paper membrane rather like this. I was sent a sample of the filter paper pleated but not made up into a filter, and it does look similar. I guess the manufacture and quality of such material has been progressing over the years.
OK, bottom line. Provided the filter material came from a reputable source! and genuinely was rated to 1 micron, I would probably be willing to trust the dual treatment approach (30 minutes) as described. It's what many have been doing for some time anyhow.
Second bottom line: It looks a whole lot cheaper than a commercial filter pump, I must say. BUT, it relies on user care to handle the filter and avoid cross-contamination. Beware of this: handle with care.
PS: while I carry a Steripen, my wife and I have given up treating most water sources, especially small side-creeks.