“...in a nutshell, a unique value needs to be crpytographically computed which then becomes the coin.”
Here is where you lost me. How do they “cryptographically compute” a value?
They wave a magic wand!
Well, I did say it is complicated. What it means it that someone is able to compute a value based on a specific set of rules (algorith) that is unique and then encrypts that value - now that it is encrypted, the value can be verified but NOT recreated by someone else (don't ask why / how) - that encrypted value is the "coin".
Academically, this is quite interesting - I would not invest in it though ...