Guild Wars 2

Signet of Domination’s passive effect is “Improved Condition Damage” which is at:

Increases condition damage by 10 + character level

according to the wiki.

I tend to run with a 1h sword in main hand, which has Mind Slash as it’s first attack, which causes Vulnerability:

Vulnerability is a condition which increases damage the target takes by 1%.

Does Signet of Domination’s passive effect have any effect on Vulnerability? Or are the Conditions that Signet of Domination’s passive effect referring to actually damaging conditions like burning, bleeding, confusion, etc, since vulnerability doesn’t actually do any direct damage?

I think you have answered your own question. Signet of Domination improves condition damage. Vulnerability is a condition that doesn’t do damage but it allows you to deal more “damage” not “condition damage”. However the condition “vulnerability” is affected by “condition duration” improvements, increasing the duration of it.