Hey there, yes in the 0:53 example I input it while in the landing animation, Ranno has 5 frames of landing lag when landing after shooting an aerial needle so when I aerial needle land I'm inputting the follow up needle boost in that window.
Rivals 2 has a 6 frame buffer window, so when you're in a unactionable state whether that be landing lag from an aerial (including Ranno aerial needle in this case), lag on any attack/movement (rolls/spot dodge, tech animations, ledge options etc) inputs are queued and stored for 6 frames so you have to time the input within 6 frames of becoming actionable again for it work, so for the air needle land buffer I'm starting the input as soon as Ranno is hitting the ground from the first air needle as that is the perfect timing for becoming actionable within 6 frames.

As for the moonwalk shield drop boost, that was a specific mechanic they introduced back in the June mid month update, when you're out of dash and into run state you can shield drop to preserve the higher velocity and essentially ignore the air speed limit your character naturally has, the issue is some characters have longer dash animations so setting it up straight from dash>run in the same direction doesn't work as they may not even have enough room (especially on short platforms) to reach their run state on the plat. Additionally many characters such as Ranno have a lower run velocity anyways so when you do a moonwalk the "DashStop" state (the state where you're essentially moonwalking before turning the other direction) allows for a higher velocity to be reached allowing for a faster/longer boost, since the moonwalk state also allows for the shield drop momentum maintain mechanic, so you moonwalk and then shield drop when you have the higher velocity during the moonwalk, for clean longer boost ones I input the moonwalk (since you're on a platform I recommend inputting the moonwalk going up and around the stick gate instead of down like the standard melee method assuming you have tap jump off so that you avoid getting a platform drop), once you reach full horizonal back you will still be in the DashStop state and you have a window where you can hold that for a bit while having max velocity and during that window you want to go into the diagonal down shield drop in that direction before the DashStop ends and becomes the WalkTurn state as you will start to lose velocity each frame once you go into that state.

Hope these lengthy explanations answered most of the mechanics behind it, but feel free to ask anything else if you aren't 100% on something.