Pretty standard instructions, for circumstances when medical help is within an hour, not mentioned in the article. The only actual treatment is anti venom. Cutting increases the risk of infection, and the liklihood is you'll miss the actual venom deposit, fangs being curved and of indeterminate length. Tourniquet reduces circulation, inhibiting dilution of the venom, and may damage otherwise healthy, uninfected tissue. Same problem with cold. Some sources recomend a tight gauze bandage a few inches above the bite, allowing circulation. Sucking, you have the problem of not necessarily addressing the venom deposit, and risk to whoever is applying the treatment if they have any abrasions in their mouth. I don't think there's any problem with using a pump which is probably smart to carry if nearby help is questionable.
You can find multitudes of conflicting advice, but no tourniquet (tight gauze instead), no cold, no cutting or sucking seem to be pretty widely accepted. And no one seems to object to pumps, though they may not be effective and often include scalpels. Within an hour or so of help, a clean wound and preventing shock is probably more important.