Welsh mountain zoo is only 15mins away, surely they would have tranq guns and staff trained to handle a variety of animals.
And almost certainly very strict legal and insurance limits on where and when they can use such things.
IIRC tranq guns are classed as firearms and you are only licensed to use them under certain conditions or on specific premises, and they will likely only have one or two trained staff (I think usually the vet) who are legally allowed to use them
Also, and this is important, to use a tranq gun safely you have to get the dosage right for the animal size and type - I suspect Zoo vets don't have a list of doses for dogs to hand.
And this all assumes that you can hit a dog that is wandering freely with the gun, in the zoos animals that are done using one are usually already confined either in a small enclosure or a cage.
So unless it was on Zoo property, or a Zoo animal it is quite possible that if they used the gun off the property they may have breached the conditions of their license and insurance.
If the dog was on a main road at 3 am in the morning then I can quite see that as much as I hate the idea, running the dog over might have been the only practical way to deal with it.
To close the road would require at least two police cars (one in both directions), which is risky in poor visibility.
To wait for a vet with a tranq gun (there aren't many in the country) could be hours, to wait for fire arms units could be hours (and have the same outcome - dead dog), dog handling units might take an hour+ and still not manage to get the dog alive.