Hey, that's me in that first video. From a few years ago.
I actually don't use that squeeze method much nowadays.
I use the fillet method for jack rabbits, and I use the method that Truduct described for cottontails, but using game shears or kitchen scissors instead of knife. My rabbit hunts only lasts 2 to 3 hours at a time, and whether or not I squeeze the guts out doesn't make any difference as far as keeping the meat fresher.
I clean them right when I get back to the car for the most part, so there is no issue of the guts sitting inside the rabbit for too long either way... The only time I would squeeze them now is if I cannot get around to cleaning them until I get home.... just to let them cool faster and avoiding the guts tainting the meat on the long drive back.
The boots are Cabelas Trekker boots, very comfortable, but I think they got discontinued a few years back.