He is not particularly big. Anyone, who has the time, (24/7 in his case) can do 100s of reps, of any form of exercise. So yes it works, but there are dozens of examples, from other people, we can use to show this. Charles Atlas for example.
I'd never exercise for vanity, so I'm not going to be judging a routine by how well it suits body builders. Nor is there a question of whether or not someone with enough time could figure out something that works, rather the idea of even reading something like this would be to shortcut one's way to something that has already been demonstrated to work. Since Bronson has set numerous records and evidently has considerable experience with maintaining physical fitness on a limited diet, in close quarters, with no access to equipment, he would seem to have at least some authority in the matter and could be a good source to consider. Not that I'd taking his word as gospel, of course...he's not a doctor, nutritionist, or personal trainer and some of his stuff seems dubious in terms of safety.
In terms of entertainment value, even a quick skim of Bronson's book suggests he'd rank higher than Atlas in this regard.
That he's self-serving and probably insane is not remotely surprising for a violent felon who has spent decades in solitary confinement, it's also neither here nor there.