For CaGI it to affect the archer, there must be a legal space adjacent for the fighter for them to be pulled to.
Assuming that's the case in your scenario, then I imagine (as I said) that the fighter leapt up and knocked them down. (Or perhaps, trying to avoid the fighter leaping up and knocking them down, the archer stumbled and fell down.)
This is why I say that it is the
critics of 4e who are obsessed by mechanics, and who seem to have trouble imagining fiction for which the mechanics is just a scaffold or a decision-making framework.
From the PHB, p 282:
During a pitched battle, heroes and monsters are in constant motion. The rogue skirts the melee, looking for a chance to set up a deadly flanking attack. The wizard keeps a distance from the enemy and tries to find a position to make the best use of area attacks, while goblin archers move to get clear shots with their bows. You can increase your effectiveness in battle by learning how to use movement and position to your advantage. . . .
A creature’s space is an expression of the number of squares it occupies.
The same page has a picture, in which a Gargantuan (4 sq x 4 sq) White Dragon has body parts (wings, neck and head, tail) that extend across a greater than 7 sq x 7 sq area.
The fact that a fighter doesn't occupy more than their single square, and doesn't move (in the technical sense) while performing CaGI, doesn't mean that they are glued to the ground. I imagine them as being in constant motion, a whirlwind of steel, similar to how REH narrates Conan.