It's short for "a ham actor," which means an bad actor, who overacts in an exaggerated way. It means someone who loves being the center of attention, and acts in an attention-getting way. In the case of a dog, it means that the dog appears to be well aware when people are paying attention to him, like attention, and does things to attract attention. "A ham even by dog standards" means that most dogs are hams. The "standard" would be the normal amount of hamminess that most dogs have. "A ham even by dog standards" means that he is even more of a ham than most dogs.

It could also mean an amateur actor. Used in this sense it is a little dated. So it means the dog was not very good at doing the tricks even for a dog. [if used in this now slightly dated but still sometimes heard sense] "he is an ham actor" = a bad actor. "the acting is ham' = the acting is amateur. what did you think of the play/film? --> it was ham. ----- What does it mean if you call someone a ham? “a bad actor who performs in an exaggerated way” or. “someone who enjoys performing and who tends to behave in an exaggerated or playful way when people are watching” Legendary actor Mickey Rooney, who died Sunday at the age of 93, referred to himself as being a ham of the latter variety.7 Apr 2014

A "ham" is basically someone who shows off in kind of a silly fun way and enjoys a lot of attention. Since dogs are known to have this type of personality in general, it's saying that this dog is even more like that than usual.

Ham = Someone who enjoys the attention of others and will do crazy things to get it. Ham = When a person is unstoppable or just int the zone in any type sport or competition setting. urbandictionary.com

I really don't know. However, I heard two days ago, there are some people got ride of their pets because they can be infected with the new corona virus and spreading the disease. What do you think?