Skyrim is real, because the game exists and we all experience the fictional world the way we choose to. We've seen caves, mammoths, sabrecats, giants, warewolves and vampires, got married, adopted children and built our own houses. We've been on many adventures around Tamriel. It may be fictional, but that doesn't make it "less real" for those of us who play and enjoying this game.
Like many rpg's out there, legends and myths of gods and goddesses are influential in the games we play and Skyrim isn't exceptional. We have the myth of Norse, Celtic and greek as an essential influence in Skyrim. Some say that there is some "reality" to the legends and myths that passed on from generation to another, with the core story almost "intact". But the longer a myth live, the interpretation of that same myth, will change over time.