Baseball rule regarding a runner running an additional base on a pop fly

Runner on first with less than 2 outs. A pop fly is hit to the outfield. Runner on first runs to second and then to third, pausing halfway to third base. Ball is caught in the outfield but the runner stays between second and third. If the ball is thrown to second base, can the second baseman/shortstop touch second base to get the runner out or do they have to throw the ball to first base?