It's not just GPU. There are not even good multicore SAT solvers. State of the art SAT algorithms are serial and they don't parallelize.
It shares short conflict clauses between parallel solvers and achieves superlinear speedup in some cases, e.g., 4 parallel solvers solve faster than one forth of the single solver soolution time.
Short conflict clauses are rare so there is little communication between solvers required.
CryptoMiniSAT: https://github.com/msoos/cryptominisat
Author's goal to have solver that is good in computing range from single CPU up to cluster. Judging from CryptoMiniSAT successes, he has mostly reached the goal.
Anyway, I believe it's similar to LP - we still use simplex method in practice, despite the fact that LP has a polynomial algorithm.
What likely happens in SAT is even though there actually is (as I believe) a nice polynomial algorithm on the order of O(n^4) or so (which involves repeated solving of linear systems), the CDCL still wins in practical problems simply because in most cases, the upfront cost of solving the equations is higher than trying to find a first solution.
However, not all hope is lost. You could actually presolve a more general problem, and then just rely on propagation to deal with a more specific instance. For instance, for integer factorization, you could presolve a general system for integers of certain bit size, and then if you wanted to factorize a specific integer, you would just plugin constants into the presolved instance. That would eliminate most of the upfront cost and bring it on par with CDCL.
Unfortunately, DIMACS is not all that good format to represent SAT, because it is not composable like this - it doesn't allow for representation of presolved instances. But composability might be a win for a different types of algorithms, which do presolving.
The 2XSAT reduction is 100% correct (I have been using it to solve small integer factoring problems), the deduction theorem proof still has a small flaw which I think is fixable, and the third part is an ongoing research which is trucking along. I will get there eventually, but if more people would be looking at this approach, then we (humanity) could arrive there faster, that's all.