Aren’t they farmed for their wool, or do people eat them too?
As I sit in pyjama
Prepared for more drama
at work, I’d be calmer
If I were a farmer
Of llama.
(Or alpaca.)
I find it unlikely that no license at all is required. It’s more likely that there is not a specific tag required, but the hunter needs to hold a ‘general hunting license’, and there are no closed seasons, or bag limits, as it’s a non-native species.
In Northwest NH, there is a private hunting preserve, from which some wild boar escaped in the 1st third of the 20th century. They established a feral colony nearby. Hunting for them is open 365 days a year. Take as many as you like… but you had better have a NH hunting license that is valid if you run into the Fish & Game guy.
Our farrier has a small but growing deer “farm” that is really taking off. He has a ton of state regs he has to adhere to and it seems like a pain in the butt, but he’s making some good money from it.
Nu?! There are starving children in Africa who would be grateful to eat that buffalo! I was in labor for 48 hours, your head was like a melon, and all you can do is argue with me?! Ptui!
OMG, it’s Pets Or Meat! 
I wrestled with doubt when I posted above - because I was sure the correct term was dovecote, but my mind kept saying “nah, dovecotes are those tiny little dove houses on poles that posh people have in their gardens”.
The other thing that only dawned on me later was - those little alcoves lining the inside of the structure - pigeonholes - the original pigeonholes.
When I was a kid, a full sized buck leaped over into our property, which was surrounded by a seven foot high fence on all sides. It ran around in there for a few minutes and then leaped over the fence again. Those damn things can really jump.
I do have some friends with a dovecote. They also have a llama and a few horses and I believe some guinea hens now (or at least they were planning on acquiring them). There are also, of course, a couple-three dogs and some rangy cats. The countryside is fun.
I know the horses are for riding, the hens are for eggs and pest control, and the llama is presumably for glaring at people. I’m not sure what the dovecote is for, though. The wife of the couple could certainly have set it up merely as a pleasant aesthetic touch – it’s on the way to the front door and everything – but her husband is a falconer. I’ve never had the heart to ask.
There are also exotic game ranches here in the US. One individual quite dedicated to historical reenactment acquired two red deer from a local ranch and turned them into a medieval feast. 