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.
The brain is slightly elastic, so you'd want to advance a needle glacially slowly (microns/second) into it so it ends up at the right position. The injection itself is also done slowly (microliters/minute) so you don't cause pressure damage.
They might also do some intraoperative imaging (some ORs have MRI or CT machines), which slows things down, and of course there's tons of cleaning and repair work afterward.
The video specifies that the drug is infused over 8-10 hours. Probe placement - again, as depicted in the video, because I don’t see a real methods section - should take about 1-2 hours. The video isn’t clear if this is interactive MRI or just a preop scan that is then loaded into a stereotactic navigation system in a regular operating room, but the former would add another hour at least. MRI is not fast.
The brain-blood barrier typically only allows small, non-polar molecules to pass through into the brain, which complicates a lot of neuro/psych treatments.
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.