If you're using Semi-Guided LRMs in the Archer, then TAGing the target allows you to ignore the target's movement modifier.
So you would calculate the to-hit number as normal for the Archer (+2 for 2 hexes of light woods, +2 for Archer running, +2 for medium range), but you would count the Stinger's movement as 0 (+0) instead of 5 (+2).
If the Archer was within range of its Medium Lasers, they wouldn't get the bonus, since TAG doesn't work for everything.