Skunk-in-the-Grass

Question
Runners on first (R1) and third (R3) with no outs. After the pitch leaves the
pitcher's hand, R1 leaves first base in a direct line to the edge of the outfield
grass between second and third (directly behind the second baseman). She
does not touch or otherwise interfere with any defensive player. Catcher runs
toward R1 and then throws the ball to the second baseman, allowing R3 to
score. R1 runs in a line directly to second base and makes it before any tag.

Is R1 out?

Answer
No.

The only time there is a defined line that a runner must take is when a fielder is attempting to make a tag on the runner.  The runner can't vary more than 3 feet from a line defined by the runners present position and the base they are heading to when the fielder is attempting a tag.  Other than this the runner can pretty much run anywhere they want on the field with a few limitations.