So is this definition wrong?
”Spur - An electrical supply using one feed cable to a socket taken off a ring main usually used to achieve an extra socket without having to do too much work.”
In this case there is no ring main. The supply is to a 6A mcb it is not from a socket, only socket will be downstream of the mc.
As far as the specifics go yes it is wrong but the essence is correct.
You will not be dealing with a ring main, we all know what you mean and understand and the vast majority of us are fairly happy to go along with the term. That should really state "ring final circuit" not "ring main".
An electrical spur can be on any circuit such as a 32A radial, a lighting circuit etc.
A spur does not have to feed a socket, I have a spur off the ring final in my kitchen to a switched fused connexion unit with a small fuse (probably less than 3A) supplying under cupboard lights, without including any socket. EDIT actually I have two of those and I use the switch as the light switch.
A spur is simply something sticking out of something else, for example a side corridor off a main corridor, it may be for hotel rooms, offices, hospital wards etc. Railway lines have spurs also known as branchlines.
So in essence your additional installation is effectively a spur and we would have recommended a fused connexion unit, however your MCB suggestion is no more, or no less ideal for the job. As both devices connect at the same place it's hard to tell which is the spur.