Out of play bases awarded?

[jeisch]

A runner is on first base, and a line drive is hit to the shortstop. The shortstop tries to double up the runner on first, who is about 10 feet off the base. The shortstop overthrows first, and he ball goes into the dugout. What base is awarded to the runner on first. The rule says the runner is awarded two bases from his position when the ball is pitched, when such wild throw is the first play by an infielder. Is the overthrow still considered the first play by the infielder, or is that the catch. Does the runner get second or third after going back and tagging up on first?