Because you said 'murder' - it's not murder. Not by any definition. Describing it as such is ignorant and thoughtless and shows how little understanding you have on both topics.
It's not about 'deserving' it's about what's right.
You've clearly never had a pet because if you had you would never think to ask this sort of question. A good, responsible, owner does no prolong an animals life for their own pleasure or enjoyment.
Arthritis in dogs is agony. As it is with humans. Even with medication, a lot are in constant pain. Just because they don't scream or cry or vocalise their pain doesn't mean it's not there. Because dogs are unable to support themselves on a particular leg or joint, they then put extra pressure on their other legs or joints - sometimes the back goes to help accommodate that - eventually they will be unable to move far if at all. It sounds like this dog is already there. It's not comfortable for any dog to live like that. And if the dogs legs are 'sticking out' as you described it - chances are it is in agony most of the time. Medication can help. But it is not a cure and it does not eradicate the pain nor the frustration the dog feels.
Dog owners (and cat, horse owners etc) know this. By this point, pretty much every responsible owner or vet will advocate for PTS - as a mercy for that dog. Most dogs with arthritis die within a couple of years - often less.
The fact this dog is old and is still going, is remarkable and is a testament to that owners love and dedication. But it does not change the fact the dog is suffering. That the owner has made that choice shows their love for their pet and your criticism and comparison to 'murder' are, IMO, judgmental, sick and unfeeling.
Lots of posters on dog house have gone through this and for to compare their final act of selfless love to murder is a disgrace.