Kjeldoran Gargoyle’s triggered ability triggers when it deals any damage, not only combat damage.

Unlike lifelink, Kjeldoran Gargoyle’s last ability is a triggered ability that goes on the stack and may be responded to. Notably, if Kjeldoran Gargoyle deals damage at the same time you’re dealt enough damage to reduce your life total to 0 or less, you’ll lose the game before you can gain any life.