I'm convinced that playing by themsleves or not is nature, not nurture. I have 2 dd's and the eldest still requires adult input at almost 4 years of age, while the younger one of 14 months plays by herself for ages and actually throws a strop if I join in when it's not required. And no I have never pandered to the eldest and given her more attention than her sister. I have actively encouraged both of them to play by themselves from a young age.
Both love imaginative play, copying what they see around them, i.e cooking, cleaning, dressing up, but dd1 is very bossy and tells me, dh and dd2 what we are supposed to be doing. even though dd2 has no clue what she is saying. Frequently hear myself and dh in dd2, she is very vocal and sounds really patronising sometimes when she talks to us, but she is only repeating what we say to her or dd2.
Dd2 is turning into a mini me, she can't talk much yet, but actions speak louder than words and it is scary to see how much like me she is already. She often plays with stuff that is supposed for older children, that her sister would not have had the benefit of like a toy cooker and toy computer.
I encourage imaginative play through providing a good range of toys and not directing their play to much. If they want to use a golf club as a walking stick or a horse, or a box as a hat or a boat, so be it. I join in with their tea parties even if dd2 does insist on making me drink directly out of the kettle, into which she has dropped play toast and is stirring with a fork!
Both really love rough and tumble type games especially with each other and playing together on the trampoline, even though I cringe when watching them as I'm sure they are going to hurt each other, there is usually lots of giggles and the thing most likely to cause tears isn't them hurting each other, but if one of them decides they don't want to play anymore. They both alos like chalk drawing on the easel.
Final observation, they always want to play with whatever the other is playing with!