My grandma also mostly plays games and checks her email/Facebook, but she also occasionally has to search the web and has used Siri on her iPad, I don't think Cortana would be that big of a stretch to get her into (e.g. I've seen her use Siri semi-regularly to check the local weather).

To be frank, she would likely be better off with a Chromebook. But unfortunately she has a few games she plays which are Windows binaries (e.g. those $5 CDs containing "2500 card games").

Cortana is no more or no less accessible than Siri.