I have something partly similar with my 10 year old DS :)
He is not a physical sporty boy anyway but he won't try new things if there's a possibility of him failing! I put it down to him being bright & most things at school come naturally to him so he hasn't really had to try at anything & he not used to finding something difficult or if there's something he can't do such as football, he would play by himself in the playground than join in a game that all his friends are playing. He would just prefer to not try than to fail.
He refuses all sports if they are not done within the family, so he's fine to go swimming with us or ride his bike round the park with us but if we are not there & its amongst his peers he just refuses. Swimming was a problem for ages as was hair washing as he screamed if his face got wet, so for a while he had to wear goggles for swimming & hair washes. He still won't shower now & insists on a bath.
Another thing is labels on clothes, he will not tolerate them next to his skin so I buy the M&S Skinkind white polo shirts for school & cut the labels out of everything else.
He's also always woken very very early & every morning since he's been in a toddler bed he has woken before 6am, even if he's had a late night he still wakes up then but is just grumpy for the whole day.
He has tics, both verbal & facial, I took him to the GP when he was about 6 & the GP said not to worry & he will grow out of them. They are short lived so for instance last week he was making a growling sound, this week its more of a coughing sound but not a cough.
I have another DS who is nothing like this but also doesn't have the cleverness academically that DS1 has. We are not a family that strives for perfection, DS1 has always known that its about trying not about winning everything so its not something we have done or encouraged. We don't connect our love with achievements. Its just him.
I have no solution but there is a thread on MN in the past year about G&T children displaying ASD traits which I found very interesting. DP & I don't really agree with our approach to him, DP thinks that we shouldn't pander & that he has to get used to labels in his clothes & just put up with it, I think there's no harm in cutting labels out, I think its a sensory issue & I don't see the benefit in keeping him uncomfortable. At the moment we do it my way but he's starting secondary in September & I'm starting to think that maybe DP's way should have more sway. I don't know, we just muddle through.
There's nothing wrong with your DD :) she's probably just a bit left of middle, wait until she asks for your help before you get involved & don't push the physical stuff, teach her to play chess or how to write stories instead. Get her to read lots. Take her to museums/art galleries/theatre etc & encourage her interests & don't focus on what she's not interested in :)