It is all about hitting. If Nick can find the groove as a hitter, he can carve out a role either with the Twins or another club as a platoon player. If their hitting is similar, Willi Castro is the better option as a utility player. Castro is a switch hitter and plays a competent third, short, second and outfield. If Gordon doesn't hit right handers at an above-average level, he really doesn't have much value to the Twins.
Gordon is extremely vulnerable to left handed pitching and isn't the Twins' preferred backup at either shortstop or third base, even with Kyle Farmer on IL. There is already an oversupply of left handed hitters in the corner outfield, so getting Nick plate appearances there is unlikely. Michael A Taylor's relative success in center also limits his chances.