It is a proof
Proof of impossibility by exhaustive examination of all possible cases is about as strong a proof as you can get since it cannot be subject to logical flaws.
It may be intellectually unsatisfying and lacking general applicability but it is still a valid proof. Hopefully at some stage in the future someone will produce a formal logic proof which casts light on the underlying structures. The fact that the validity or otherwise of the conjecture is now established may actually help this process in that future workers will know what they need to (dis)prove. This has happened before with computer proofs.