It seems 'Takes damage' is only available for 'Specific Unit Event'. To use it for all units on the map you will need to add the event when each unit is created:
Trigger:
Unit Registration 1
Events
Map initialisation
Actions
Unit Group - Pick every unit in (Units in Playable Map Area) and do (Trigger - Add to (Unit Damaged <gen>) the event (Unit - Picked unit Takes damage))
Trigger:
Unit Registration 2
Events
A unit enters Playable map area
Actions
Trigger - Add to (Unit Damaged <gen>) the event (Unit - Entering unit Takes damage)
Replace 'Unit Damaged <gen>' with whatever trigger you are using to handle damage. In this trigger you can get the amount of damage taken as a Real number using the function 'Event Response - Damage Taken'. If the damage was done by a unit or building, this unit will be 'Event Response - Damage Source'.
I'm on a page about incorrect corrections, and spent the better part of like two hours trying to get someone to understand that -5^2 = -25, not 25, and then that post had comments get reposted because that group is self sustaining, and that person was in turn trying to explain what I just explained to them. And I'm taking that as a victory
I will be AFK for a couple of days you guys hold down the fort while I am gone. I will be checking in on my phone but that will severly limit me. Be back saturday!