I'm not going to go into a lengthy response because that website is typical pseudo-science BS. Any website that makes an appeal to fear by citing chlorine gas as being used in WWI to kill people is not a rational website. Obviously it is someone trying to promote an "alternative to chlorine" position. It would be a waste of my time to discuss anything that site has to say and it has all been covered here on TFP.
Peroxide can NOT be used as a method of pool/spa sanitation because it is not possible to maintain a high enough residual peroxide level to be practical. The EPA only recognizes three chemicals as pool sanitizer - chlorine, bromine and Baquacil. Peroxide is not one of them. Peroxide would have to be held at concentrations of nearly 50-100ppm to even come close to the CT kill times associated with chlorine/bromine. That is well above the threshold that would be very irritating to eyes and skin.
Peroxide can be used to regenerate bromine from the bromide bank in a spa but it is less effective that just using chlorine bleach to do so. If one wanted to have a spa with no halogens in it, then one could use the Nature2 system (silver ions) in conjunction with MPS as an oxidizer. But that will be very expensive and bather waste will likely take longer to oxidize. In a Nature2 system you'd want to have a UV sanitizer system as well to help with the bather waste.