Children are different - I adore the fact my 7 year old can play alone for hours - but if his brother is home he gets annoyed with him because 7 year old makes endless sound effects :o I find him a joy because he doesn't require endless full on focussed attention, though every so often I have to listen attentively to a monologue or watch something. He also has a best friend who I could happily adopt :o - he comes over for 24 hours including a sleepover as they're at different schools and don't see each other in the week. They're no bother at all and only need feeding and reminding to put coats on if they decide to play out, reminding to brush teeth and go to bed etc.
Dc2 has also been easy as he wants to play football endlessly, and we're lucky to live near green space and lots of kids to play with. There were a couple of years when I had to spend too much time kicking balls at him though (goalie) as he'd wear even his friends and dc1 out.
My eldest is nearly 13 and has always needed focussed attention and to be played with. She's never properly been an only as I was childminding full time from when she was 10 months old til dc2 was born when she was only just 2. She does however play brilliantly with peers and her siblings, from 3-11 we had her friends here all the time and she was no trouble. One of the reasons I'm finding the almost teen age hard is she suddenly wants more from me again - I was expecting her to become more self sufficient with age, but she wants to play board and card games and wants me to watch films with her whenever were alone together - I was hiding in my room reading or with my friends at her age and I admit I don't totally get it... She's just more sociable than me and the personality difference can make the demands waring.
People who say "can't you just do things with her, I think it's nice" don't understand that kids like this are just as unhappy if you play with them for an hour then stop, they don't get that you need your own headspace at all, so feel rejected even when you play with them for hours but then want a bit of space.
I do think the whining when on walks and the unsuccessful play dates sound like spoilt behaviour though and would sit down and lay down some ground rules there.
We handled that age by making sure she constantly had friends to play with, never saying no to a manageable play date or friends coming in, though she was also very close to dc2 while they were both small.
Perhaps the playdates are too rare for her to be in the rhythm and know what to do? Or perhaps you need to try a few different friends to find a compatable one - no need to make life harder having a difficult guest too!