You have obstruction which entitles him 1st base. He obtained 1st base on his own, therefore, obstruction is ignored and the play goes on. Since the ball went into dead ball territory, he is given 2nd base.
Question- If he had thrown it 3 feet over 1st basemen's head and no obstruction occured, you would still give him 2nd base, right? Same here. The only way obstruction needs to be called is if the 1st baseman obstructed the runner and he was out.
On this play, you could have interference if the batter-runner is out of the running lane or obstruction if he is in the running lane. Thats why plate man needs to be at the 45 ft line up 1st base line.