Welcome to my world BB.
I run machines that do this daily for my living- EDM.
EDM is short for, as others mentioned, Electrical Discharge Machining. It is the only technology that makes specifically the kind of Parts you saw in that video possible. No other process can create perfect shapes that mesh so perfectly this way they appear seamless. I don’t care how good of a machinist you are it is physically impossible to do with traditional machining techniques what you saw. Maybe grinding for simple shapes, but none of these shapes apply (though there are 3d grinders, this was all electropolished EDM work).
There are two kinds of EDM- ram and wire. Wire cuts are exactly like an electrical cheese cutter using 0.005" or bigger wire- to slice perfect finished parts. But true sharp internal corners are impossible, due to a wire always having a radius. Ram EDM is what I run- no wire- just a 3D shape on a block of graphite or cuprotungsten, and it burns the shape into a block of conductive material.
You can make shapes otherwise impossible to cut with rotating tools, or machine things impossible to cut, like I do- superhardened die steel blocks turn into titanium forging dies for aerospace parts and artificial bones. Only thing is, material you burn must be conductive.
Other, ultra rare stuff, like LIGA and ultrasonic milling exists, but this kind of thing was definitely made with EDM. This is a level beyond what I work to- fits like this are tolerances of 0.00005" or so I’d guess. At most, I work to 0.0001-0.0002".
I love seeing parts fit so perfectly like this, so satisfying!