There's not much on that first video you couldn't do with many of the smaller (though they aren't small) Mastiff breeds, not to discredit the dog for his drive to do what he was taught.
With that said a dog shouldn't be jumping off things, just like humans their joints have limits and they aren't designed by nature to take those kind of falls over and over.. that's a huge impact and load on their joints.. can they do it? Sure, will it cause issues down the road? You better believe it.
Mike mentioned training them up from a puppy and having their joints adapt.. the issue with that is nature doesn't work that quick. Like many other animals, if the animal is exposed to something over a given period of time or a task, it can developed traits to aid it in that exposure or task. That doesn't however work over the course of a dogs life, what you'd end up with is a dog with mobility issue's early due to the extreme load put on it's joints.
Same reason I have knee issue's, I started skating as a 7 year old.. jumping of things, acting crazy etc. This progressed into aggressive inline skating thru my early 20's. Your joints break down, they don't adapt.
There's a number of studies out there on working K9's and their training associated with scaling & jumping.. as they have to be kept up to par thru there duty on training/apprehension work. Just as everything else does it takes a toll on the dogs, but it's apart of what they do in their line of work.
The issue you'd run into with Mastiff's is the force is greatly multiplied in our dogs when they jump off thing because of the sheer weight. My male EM has a great vertical jump, and can hit chest high walls without issue.. I don't allow him to jump off them however. I will pick him up and put him on the ground, and one day my back will give out from this also lol.
