The major hurdle of current gene therapies is delivery to the tissue where the defective gene product is causing damage. For instance lipid nanoparticles are only being used to deliver gene therapies to the liver, because if you inject them they just end up there and not much anywhere else. In this case they are using an virus called "adeno asociated virus 5" (AAV5), which does not naturally infect the brain AFAIK. The blood brain barrier (basically just extra impermeable blood vessels), as well as other immunological features in brain tissue, evolved specifically to keep the brain as unaffected as possible from anything bad going on in the body, seeing as any infection/poisoning of the brain is varying degrees of catastrophic and would easily kill you in the ancestral environment.

I don't know the details of why AAV5 in particular is their vector of choice in this case, but for whatever reason thats what they've gone with. AFAIK there are no viral or other vectors that consistently infect all brain tissue when injected/ingested, so maybe that's just the best option available. Anyways, it seems that in order to get it to the actual brain tissue that is damaged by the huntington protein (all of it? One particular area?), the best way is to inject it where it needs to go. If you could just pump it into the CSF that would perhaps make things a little bit more tolerable, seeing as you could then just do a spinal tap and inject it that way, but apparently that doesn't work. Or maybe a generalized AAV5 infection has more side effect then targeted injections. Just speculating here.