Problem is when its the other way around. THEN initiative matters.
If warlock has deathlink on a highland unicorn with regen that has 2 life left.
When the warlock has initative he can choose to resolve his deathlink before the horse gets to regen.
That's correct.
Santar and Hagen currently seem to think that each effect triggers in initiative order.
But that's not correct.
All effects trigger
at the same time.
Only the resolution of those effects are made in initiative order.
Meaning :
The mage with initiative chooses 1 of his objects and resolves
all effects on it in the order he chooses ( so, for example, lifelink first, then idol )
Then he chooses another of his objects that has effects on it and resolves those in the order he chooses...
and so on until he has no more objects with upkeep effects on them.
Then the player who does not have initiative does the same.
So this means that it is possible, as Jacksmack points out, that the Player with initiative chooses to use his Death Link first but in the process of doing that kills the opposing player's Unicorn before that one can regenerate.