A deliberate all gear up landing in a big jet is expected to almost always end happily for the crew. Passengers may have more of an issue with evacuations, and even more so for unnecessary evacuations. Somebody always at least twists an ankle. Good to see this one came out nominally.
I used to fly 757s and still have the books. A quick review says the normal hydraulic extension system is backed up by a separate hydraulic pump and fluid supply. The relevant emergency procedures suggest landing on whichever gear have extended in preference to trying to retract a partial gear situation in favor of an all gear up landing. So we can conclude the malfunction itself caused a complete failure to extend. Having both systems fail independently on all 3 gear seems highly improbable to me. Suggesting a common cause.
757s and older Boeings have 3-position gear levers: [Up], [Off], & [Down]. [Up] and [Down] are self-explanatory. [Off] is selected in flight shortly after retraction completes. It isolates the whole gear system from the hydraulics. The gear are retained in the retracted position by over-center mechanical locks. For landing, the handle is moved to [Down], pressure is applied to the extend side of all the mechanisms, and down comes the gear. Normally.
As an aside, newer Boeings (777 and subsequent plus 737 Max) have a two-position electrical gear switch replacing the old fashioned big heavy mechanical 3-position handle. Internally the same [Off] functionality is implemented by timers & solenoid valves after retraction completes.
There have been failures on various airplanes in the past where the gear lever gets mechanically disconnected from the hydraulic valve it controls. Or the valve itself gets stuck. If this occurs post takeoff in the course of retraction, the handle or valve may be stuck in the up position, holding hydraulic pressure to the upside. That has resulted in the inability to extend the gear by either normal or alternate means, regardless of how the alternate feature works on that airplane type. Turning off the hydraulic system(s) which power the gear might be a possible work-around for that but is not part of the published gear failure procedures. John Wayne might have tried that, but he died a long time ago now.
Something in that general line of thinking is probably the most likely cause for this event. I doubt we’ll ever get much more detail, but it would be interesting to learn about.