I understand that. The author himself does not claim this approach is faster than bruteforce. Indeed, consider the converse: for mining using a SAT solver to be faster than bruteforce implies that the SAT solver is able to exploit some structure in the hash function which plain bruteforce has no access to. The point of a good hash function is to have no such structure.

If you additionally consider how SAT solving algorithms work, they are less amenable to modern CPUs than plain bruteforce, which can take full advantage of SIMD and instruction parallelism. If you look at password hash breakers, you will see them using extra tricks, like early abort, to speed things up even further.

That is equivalent to breaking SHA, if you consider a partial preimage attack a weakness, which I'd say many cryptographers do.