I don't remember my Mother playing much with me - she was hot on reading and writing and academic stuff (she was a teacher) but we were sent out to play/played on our own indoors with lego etc . There was no internet, no twitter, not even a landline until I was 8 or 9.
Kids need to learn to play on their own - stimulates their imagination if they have to think a bit for themselves!!
When mine were small I had no internet or mobile and did play with them to a certain extent. But I found it so utterly boring. Loved reading to them, singing, that kind of things, but craft, model making, "pretend games" left me very cold.