Earlier this year someone on hfboards made a video of Barkov's every shift in a game. It's not a highlight reel and his team Tappara doesn't play an exciting type of game (and neither does the opponent, Ortio and Granlund's HIFK), but it is very good if you want to evaluate his positioning, passing, etc. Also he plays with Nemo. Easy to spot with the golden helmet.
Three periods:
http://www.youtube.com/watch?v=PzuooNUm8BM
http://www.youtube.com/watch?v=I1kxLsvD_ig
http://www.youtube.com/watch?v=MFVxuQlh-6g