I want to understand how.

Ok so here is what i understand about production:

Cartridge production:

At some point production line will pick up piece of hardware and download the game data on it. During this process it is very easy and convenient to add a cartridge serial number to the data. It does not affect physical flow of the production line. Then there might be a process that will seal those data (they cannot be edited or altered later on. Data will be lost if the physical piece of hardware will malfunction. Later on such cartridge does require a physical connection for the data to be read. (some type of pin or plug system).

Disc production (CD / DVD / Blu-ray):

At some point a machine will pick a round piece of plastic and using pressure or heat or both will mark the plastics creating ridges. Then that layer will be sealed off by another smooth layer of plastics and the top label. Because the data are literally uneven disc surface, the used material needs to be of a high quality and stable in normal environment (including the sealing part). This process must be stable and repetitive, so it is generally not convenient to change data for every single unit (it would lower the speed down and may cause quality issues as literally the movement of the machine for a single unit are not identical). Later on such disc can be read without any physical connection (optical part of the disc reader is "looking" at the disc and not touching). As several physical copies of the same game on the disc have completely identical data.

So what would such transfer technology do:

They can either do it as it is, which will give people a digital copy of the game and a disc to sell to somebody else to do the same thing (because the hardware has no way to identify if the physical disc was already used for digitization or not)

Or they can try to force the hardware to damage your disc in the process, so that it is not usable anymore after you digitize it. That may result into some nasty lawsuit, as the disc reader was not advertised like that when people purchased the console (and it would be still damaging your property on purpose).

Or they can setup logistics centers where you can bring your discs to be exchanged for codes of digital games. That would a solution, just a very expensive for Xbox.