I tested it on target dummy in town, after changing Warrior subclass to Tyrant.
Chains' skill damage stays the same regardless of how many points you put in the Chains skill.
Other skills for other classes will scale instantly after investing points, but not this one. So this is a bug.
Chains damage scales fine with Ruthlessness points, but it should scale with both Chains and Ruthlessness skill points.
So there is currently no reason to put more than 1 point into the Chains skill, since skills point don't scale the damage at all.
(Side note: I posted this on Steam forums yesterday, posting it here as well, in case Discord is better for Devs to notice this bug post)