Every dog is different. My parents got their Yorkie from a breeder when he was about 3 years old. He had been picked on by the bigger dogs (and probably not treated very well by the humans either). He is now 13 and never really learned to play.
I got both of mine a year ago. Prince was 5 and Angel was about 2 1/2. Prince started playing the first night I brought him home. Angel has just started playing in the past month or so. She will play with me or sometimes with Prince, but not with toys. She hovers over them but doesn't play with them. She is very small and I think they carried her everywhere. I don't think she had much time to play - but she sure learned to snuggle!
I see my parents at least a couple of times a month. Now that their dog is exposed to other dogs his size he is learning to play a little bit. He won't play with them but Mom says he does something new a day or two after they visit. She says it looks like he is trying to imitate some of the things they do.