My son now just 4yrs was like that at about age 2yrs. Wanting to spend time alone. This is what led us down the path to a diagnosis (PDD-NOS/Aspergers).
We met a wonderful psychologist when he was 2yrs, who told us to 'bring' him into family life as much as possible. She advised us not to leave him on his own, even if you are present in the room comenting on what she is doing, keeping him connected with 'normality'. We followed this advice every day, we were worn out. As you said it is soul destroying trying to interact all the time and getting nowhere.
But we continued with it, never forcing him to engage if he didnt want to, but just being with him, showing him you are there even if only in your presence. My son now is very sociable, loves to be around people, we do give him some down time, but we watch him and if he seems to be really 'switching off' we sit with him and comment on what he is doing, like a sportscaster. Right away we have him back with us, and he is not pressureised to say anything or interact if he isnt ready.
That was the most valuable piece of advice we have been given, I dont think it would be good for any childs development to watch videos alone for any length of time. We all need a break and allow them to do this at some point in the day, but maybe try to reduce it slowly.
Thats wonderful that she can talk, and understand language, so you have an advantage to try and break through into her little world. I suppose we were affraid if left in that little world too long, it would be harder to come out as time goes by.
When they are young is the best time to try to mould them. I hope this helps, obviously you will have to be guided by her and if she gets stressed with the company of others. Although I would still slowly try to increase the time she spends with others, it really will benefit her in the long run, because life is full of people.
Good Luck xx