I'm also unclear as to how basic inferential logic puzzles spells out intelligence

I think if you summed up measures of intelligence as 'can it do basic symbolic logic in a chain with memory' then yes, you've now achieved the intelligence of an e. coli colony [0], congratulations

[0] https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.03...

> basic inferential logic puzzles spells out

It spells out a form of intelligence - some can and some cannot.

Those puzzles are an abstraction of a skill which is thought to be exportable in other domains.