Rob, I think both of those were best described as April Fool's jokes. The centrifuge idea has been around for a while and could work in theory but IIRC the last time it came up here the calculations for how big it needed to be--on a scale from small to big--was "Yankee stadium". It wouldn't fit on your back.
The Hollywood prop is cute but it relies on somehow or other (undefined) separating dissolved oxygen from the water (kind of like the centrifuge idea) and then "compressing" it with a "microprocessor" and "micro" battery. LOL. The inventor evidently doesn't realize that "compressing" is done with a "pump". I'll be curious to see what kind of form his contraption will take once he realizes he needs to drive a pump with a micro-battery.
No discerning reader is going to believe either idea, TBH. For the author's purposes, it would be more believable in a science fiction setting if the divers had tanks that could be pumped up to 10,000 bar.
R..
I know they're not real. If they were everyone would be diving them already. But for the purpose of a fiction writing I thought it might give the authors something to consider in developing their own gills.